Reflection — Multiple Choice Questions

The distance of the point P(-3, -4) from the x-axis is :

1. 3 units

2. 4 units

3. 5 units

4. none of these

Answer

The distance of any point (x, y) from the x-axis is given by the absolute value of the y-coordinate, |y|.

For the point P(-3, -4), the distance from the x-axis is |-4|.

Distance = 4 units.

Hence, Option 2 is the correct option.

The distance of the point A(-6, 8) from the y-axis is :

1. 8 units

2. 10 units

3. 6 units

4. none of these

Answer

The distance of any point (x, y) from the y-axis is given by the absolute value of the x-coordinate, |x|.

For the point A(-6, 8), the distance from the y-axis is |-6|.

Distance = 6 units.

Hence, Option 3 is the correct option.

A point lies on the x-axis at a distance of 5 units from the y-axis to the left side of the origin. The co-ordinates of this point are :

1. (0, 5)

2. (0, -5)

3. (5, 0)

4. (-5, 0)

Answer

A point lying on the x-axis has a y-coordinate of 0.

A distance of 5 units from the y-axis means the x-coordinate is ± 5.

"To the left side of the origin" implies the x-coordinate is negative.

Therefore, the co-ordinates of the point are (-5, 0).

Hence, Option 4 is the correct option.

A point lies on the y-axis at a distance of 3 units below the x-axis. The co-ordinates of this point are :

1. (0, 3)

2. (0, -3)

3. (3, 0)

4. (-3, 0)

Answer

A point lying on the y-axis has an x-coordinate of 0.

A distance of 3 units means the y-coordinate is ± 3

"3 units below x-axis" implies the y-coordinate is negative.

Therefore, the co-ordinates of the point are (0, -3).

Hence, Option 2 is the correct option.

What does the line x = -4 represent?

1. A line parallel to the x-axis at a distance of 4 units above the x-axis.

2. A line parallel to the x-axis at a distance of 4 units below the x-axis.

3. A line parallel to the y-axis at a distance of 4 units to the left of the y-axis.

4. A line parallel to the y-axis at a distance of 4 units to the right of the y-axis.

Answer

An equation of the form x = k represents a straight line parallel to the y-axis.

Since k = -4, the line is 4 units away from the y-axis to the left.

Hence, Option 3 is the correct option.

What does the line y = 8 represent?

1. A line parallel to the y-axis at a distance of 8 units to the left of the y-axis.

2. A line parallel to the y-axis at a distance of 8 units to the right of the y-axis.

3. A line parallel to the x-axis at a distance of 8 units below the x-axis.

4. A line parallel to the x-axis at a distance of 8 units above the x-axis.

Answer

An equation of the form y = k represents a straight line parallel to the x-axis.

Since k = 8, the line is 8 units away from the x-axis above it.

Hence, Option 4 is the correct option.

Reflection of point P(a, b) in x-axis is :

1. P'(a, b)

2. P'(-a, b)

3. P'(a, -b)

4. P'(-a, -b)

Answer

Reflection in the x-axis is given by the transformation

R_x(x, y) = (x, -y)

Applying this rule to P(a, b):

P(a, b) ⇒ P'(a, -b)

Hence, Option 3 is the correct option.

Reflection of point P(a, b) in y-axis is :

1. P'(a, b)

2. P'(-a, b)

3. P'(a, -b)

4. P'(-a, -b)

Answer

Reflection in the y-axis is given by the transformation

R_y(x, y) = (-x, y)

Applying this rule to P(a, b):

P(a, b) ⇒ P'(-a, b).

Hence, Option 2 is the correct option.

Reflection of point P(a, b) in the origin is :

1. P'(a, b)

2. P'(-a, b)

3. P'(a, -b)

4. P'(-a, -b)

Answer

Reflection in the origin is given by the transformation

R_o(x, y) = (-x, -y)

Applying this rule to P(a, b):

P(a, b) ⇒ P'(-a, -b)

Hence, Option 4 is the correct option.

The image of the point P(-5, -6) when reflected in the x-axis is :

1. (5, -6)

2. (5, 6)

3. (-5, -6)

4. (-5, 6)

Answer

Reflection in the x-axis changes the sign of the y-coordinate only, while the x-coordinate remains the same.

Applying this rule to (-5, -6):

(-5, -6) ⇒ (-5, 6).

Hence, Option 4 is the correct option.

The coordinates of the point P(-3, 5) on reflecting on the x-axis are :

1. (3, 5)

2. (-3, -5)

3. (3, -5)

4. (-3, 5)

Answer

Reflection in the x-axis changes the sign of the y-coordinate only, while the x-coordinate remains the same.

Applying this rule to (-3, 5):

(-3, 5) ⇒ (-3, -5)

Hence, Option 2 is the correct option.

The image of the point A(3, 4) when reflected in the y-axis is :

1. (3, -4)

2. (-3, 4)

3. (-3, -4)

4. (3, 4)

Answer

Reflection in the y-axis changes the sign of the x-coordinate only, while the y-coordinate remains the same.

Applying this rule to (3, 4):

(3, 4) ⇒ (-3, 4).

Hence, Option 2 is the correct option.

The reflection of the point A(4, -7) in the y-axis is :

1. (4, -7)

2. (-4, 7)

3. (4, 7)

4. (-4, -7)

Answer

Reflection in the y-axis changes the sign of the x-coordinate only, while the y-coordinate remains the same.

Applying this rule to (4, -7):

(4, -7) ⇒ (-4, -7).

Hence, Option 4 is the correct option.

The image of the point (-7, 8) when reflected in the origin is :

1. (-7, 8)

2. (-7, -8)

3. (7, -8)

4. (7, 8)

Answer

Reflection in the origin changes the sign of the y-coordinate and x-coordinate.

Applying this rule to (-7, 8):

(-7, 8) ⇒ (7, -8)

Hence, Option 3 is the correct option.

The reflection of the point (4, -11) in the origin is :

1. (-4, 11)

2. (-4, -11)

3. (4, 11)

4. (4, -11)

Answer

Reflection in the origin changes the sign of the y-coordinate and x-coordinate.

Applying this rule to (4, -11):

(4, -11) ⇒ (-4, 11)

Hence, Option 1 is the correct option.

Which of the following points is invariant under reflection in the x-axis?

1. (-3, 4)

2. (7, -6)

3. (0, -4)

4. (-5, 0)

Answer

A point is invariant under reflection in the x-axis if the point lies on the x-axis. A point lies on the x-axis if its y-coordinate is 0.

The only point with a y-coordinate of 0 is (-5, 0).

Hence, Option 4 is the correct option.

Which of the following points is invariant under reflection in the y-axis?

1. (14, 0)

2. (0, 8)

3. (-12, 3)

4. (4, -5)

Answer

A point is invariant under reflection in the y-axis if the point lies on the y-axis. A point lies on the y-axis if its x-coordinate is 0.

The only point with an x-coordinate of 0 is (0, 8).

Hence, Option 2 is the correct option.

Which of the following points is invariant with respect to the line y = -2?

1. (2, 3)

2. (-3, 2)

3. (-2, 3)

4. (3, -2)

Answer

Since, in (3, -2), y = -2, it means this point lies on the line. Hence, it a invariant point.

Hence, Option 4 is the correct option.

Reflection of P(a, b) in x-axis followed by the reflection in y-axis is :

1. (a, b)

2. (-a, b)

3. (a, -b)

4. (-a, -b)

Answer

We know that,

On reflecting in x-axis the sign of y co-ordinate changes.

Let on reflection in x-axis the point P(a, b) becomes P'.

P(a, b) ⇒ P'(a, -b).

We know that,

On reflecting in y-axis the sign of x co-ordinate changes.

On reflection in y-axis point P'(a, -b) becomes P".

P'(a, -b) ⇒ P"(-a, -b).

Hence, Option 4 is the correct option.

Reflection of P(a, b) in y-axis followed by reflection in x-axis is :

1. (-a, b)

2. (a, -b)

3. (-a, -b)

4. (a, b)

Answer

We know that,

On reflecting in y-axis the sign of x co-ordinate changes.

Let on reflection in y-axis point P(a, b) becomes P'.

P(a, b) ⇒ P'(-a, b).

We know that,

On reflecting in x-axis the sign of y co-ordinate changes.

Let on reflection in x-axis point P'(-a, b) becomes P".

P'(-a, b) ⇒ P"(-a, -b).

Hence, Option 3 is the correct option.

Reflection of P(a, b) in x-axis followed by reflection in origin is :

1. (a, b)

2. (-a, -b)

3. (-a, b)

4. (-a, -b)

Answer

We know that,

On reflecting in x-axis the sign of y co-ordinate changes.

Let on reflection in x-axis point P(a, b) becomes P'.

P(a, b) ⇒ P'(a, -b).

We know that,

On reflecting in origin the sign of both x and y co-ordinate changes.

Let on reflection in origin point P'(a, -b) becomes P".

P'(a, -b) ⇒ P"(-a, b).

Hence, Option 3 is the correct option.

Reflection of P(a, b) in y-axis followed by reflection in origin is :

1. (-a, -b)

2. (a, b)

3. (-a, b)

4. (a, -b)

Answer

We know that,

On reflecting in y-axis the sign of x co-ordinate changes.

Let on reflection in y-axis point P(a, b) becomes P'.

P(a, b) ⇒ P'(-a, b).

We know that,

On reflecting in origin the sign of both x and y co-ordinate changes.

Let on reflection in origin point P'(-a, b) becomes P".

P'(-a, b) ⇒ P"(a, -b).

Hence, Option 4 is the correct option.

The co-ordinates of the point (4, -7) when reflected in the x-axis followed by the reflection in the y-axis is :

1. (4, -7)

2. (-4, 7)

3. (4, 7)

4. (-4, -7)

Answer

Given,

Let the point (4, -7) be P.

We know that,

On reflecting in x-axis the sign of y-co-ordinate changes.

Let on reflection in x-axis, P(4, -7) becomes P'.

P(4, -7) ⇒ P'(4, 7).

We know that,

On reflecting in y-axis the sign of x-co-ordinate changes.

Let on reflection in y-axis P'(4, 7) becomes P".

P'(4, 7) ⇒ P"(-4, 7).

Hence, Option 2 is the correct option.

The co-ordinates of the image of the point (-6, 9) when reflected in y-axis followed by the reflection in x-axis is :

1. (-6, 9)

2. (6, 9)

3. (-6, -9)

4. (6, -9)

Answer

Given,

Let the point (-6, 9) be P.

We know that,

On reflecting in y-axis, the sign of x-co-ordinate changes.

Let on reflection in y-axis, P(-6, 9) becomes P'.

P(-6, 9) ⇒ P'(6, 9).

We know that,

On reflecting in x-axis the sign of y-co-ordinate changes.

Let on reflection in x-axis, P'(6, 9) becomes P".

P'(6, 9) ⇒ P"(6, -9).

Hence, Option 4 is the correct option.

The co-ordinates of the image of the point (-5, -8) when reflected in y-axis followed by the reflection in origin is :

1. (-5, 8)

2. (5, -8)

3. (-5, -8)

4. (5, 8)

Answer

Given,

Let the point (-5, -8) be P.

We know that,

On reflecting in y-axis the sign of x-co-ordinate changes.

Let on reflection in y-axis, P(-5, -8) becomes P'.

P(-5, -8) ⇒ P'(5, -8).

We know that,

On reflecting in origin the sign of both x and y co-ordinate changes.

Let on reflection in origin, P'(5, -8) becomes P".

P'(5, -8) ⇒ P"(-5, 8).

Hence, Option 1 is the correct option.

The co-ordinates of the image of the point (7, 11) when reflected in x-axis followed by the reflection in origin is :

1. (-7, 11)

2. (7, 11)

3. (-7, -11)

4. (7, -11)

Answer

Given,

Let the point (7, 11) be P.

We know that,

On reflecting in x-axis the sign of y co-ordinate changes.

Let on reflection in x-axis, P(7, 11) becomes P'.

P(7, 11) ⇒ P'(7, -11).

We know that,

On reflecting in origin the sign of both x and y co-ordinate changes.

Let on reflection in origin, P'(7, -11) becomes P".

P'(7, -11) = P"(-7, 11).

Hence, Option 1 is the correct option.

The point P(-14, -18) is reflected in origin and after that reflected in x-axis. The co-ordinates of the image of point P are :

1. (-14, -18)

2. (14, -18)

3. (-14, 18)

4. (14, 18)

Answer

We know that,

On reflecting in origin the sign of both x and y co-ordinate changes.

Let on reflection in origin P(-14, -18) becomes P'.

P(-14, -18) ⇒ P'(14, 18).

We know that,

On reflecting in x-axis, the sign of y co-ordinate changes.

Let on reflection in x-axis, P'(14, 18) becomes P".

P'(14, 18) ⇒ P"(14, -18).

Hence, Option 2 is the correct option.

The point P(-7, 13) is reflected in origin followed by reflection in y-axis. The co-ordinates of the image of point P are :

1. (7, 13)

2. (-7, -13)

3. (7, -13)

4. (-7, 13)

Answer

We know that,

On reflecting in origin the sign of both x and y co-ordinate changes.

Let on reflection in origin, P(-7, 13) becomes P'.

P(-7, 13) ⇒ P'(7, -13).

We know that,

On reflecting in y-axis, the sign of x co-ordinate changes.

Let on reflection in y-axis, P'(7, -13) becomes P".

P'(7, -13) ⇒ P"(-7, -13).

Hence, Option 2 is the correct option.

If the point P(a, b) is reflected in the x-axis to P'(3, -7), then the value of (a - b) is :

1. 10

2. -10

3. 4

4. -4

Answer

Given,

Co-ordinates of point P = (a, b) and P' = (3, -7).

We know that,

On reflecting in x-axis, the sign of y co-ordinate changes.

∴ (a, b) ⇒ (a, -b)

Given,

P(a, b) is reflected in the x-axis to P'(3, -7).

∴ (a, -b) = (3, -7)

⇒ a = 3 and -b = -7

⇒ a = 3 and b = 7.

Thus, a - b = 3 - 7 = -4.

Hence, Option 4 is the correct option.

If the point P(a, b) is reflected in the y-axis to P'(-3, -9), then the value of (a + b) is :

1. -6

2. 6

3. -15

4. -12

Answer

Given,

Coordinates of P(a, b) and P'(-3, -9).

We know that,

On reflecting in y-axis the sign of x co-ordinate changes.

∴ (a, b) ⇒ (-a, b)

Given,

P(a, b) is reflected in the y-axis to P'(-3, -9)

∴ (-3, -9) = (-a, b)

⇒ -a = -3 and b = -9

⇒ a = 3 and b = -9.

∴ a + b = 3 + (-9) = 3 - 9 = -6.

Hence, Option 1 is the correct option.

If the point P(a, b) is reflected in the origin to P'(7, -13), then the value of (a - b) is :

1. 20

2. 6

3. -20

4. -6

Answer

Given,

Co-ordinates of point P = (a, b) and P' = (7, -13).

We know that,

On reflecting in origin the sign of both x and y co-ordinate changes.

∴ (a, b) ⇒ (-a, -b)

Given,

P(a, b) is reflected in the origin to P'(7, -13)

∴ (7, -13) = (-a, -b)

⇒ -a = 7 and -b = -13

⇒ a = -7 and b = 13.

∴ a - b = -7 - 13 = -20.

Hence, Option 3 is the correct option.

If the point P(a, b) is first reflected in the origin and then reflected in the x-axis to the point P"(12, -5), then the value of (b - a) is :

1. -17

2. 17

3. 7

4. -7

Answer

Given, point P(a, b).

On reflection in origin, sign on both coordinate changes.

(a, b) ⇒ (-a, -b)

On reflection in x-axis, the sign of y-coordinate changes.

(-a, -b) ⇒ (-a, b)

Given, final point P'(12, -5).

∴ (-a, b) = (12, -5)

⇒ -a = 12 and b = -5

⇒ a = -12 and b = -5.

⇒ b - a = -5 - (-12) = -5 + 12 = 7.

Hence, Option 3 is the correct option.

If the point P(a, b) is first reflected in the origin and then reflected in the y-axis to the point P"(-9, -7), then the value of (2a - 3b) is :

1. -16

2. -25

3. -3

4. -39

Answer

Given, point P(a, b).

On reflection in origin, the sign of x-coordinate and y-coordinate changes.

(a, b) ⇒ (-a, -b)

On reflection in y-axis, the sign of x-coordinate changes.

(-a, -b) ⇒ (a, -b)

Given, final point P'(-9, -7)

∴ (a, -b) = (-9, -7)

⇒ a = -9 and -b = -7

⇒ a = -9 and b = 7

⇒ 2a - 3b = 2(-9) - 3(7)

⇒ -18 - 21

⇒ -39.

Hence, Option 4 is the correct option.

If the point P(a, b) is first reflected in the x-axis and then reflected in the origin to the point P"(-8, -2), then the value of (a - 2b) is :

1. -12

2. 12

3. 10

4. -10

Answer

Given, point P(a, b).

On reflection in x-axis, the sign of y-coordinate changes.

(a, b) ⇒ (a, -b)

On reflection in origin, the sign of x-coordinate and y-coordinate changes.

(a, -b) ⇒ (-a, b)

Given, final point P'(-8, -2)

∴ (-a, b) = (-8, -2)

⇒ -a = -8 and b = -2

⇒ a = 8 and b = -2

⇒ a - 2b = 8 - 2(-2)

⇒ 8 + 4

⇒ 12.

Hence, Option 2 is the correct option.

If the point A(p, q) is first reflected in the y-axis and then reflected in the origin to the point A"(-6, 15), then the value of (2p + 3q) is :

1. -57

2. -21

3. 43

4. 57

Answer

Given, point A(p, q).

On reflection in y-axis, the sign of x-coordinate changes,

(p, q) ⇒ (-p, q)

On reflection in origin, the sign of x-coordinate and y-coordinate changes,

(-p, q) ⇒ (p, -q).

Given,

Final coordinates = A"(-6, 15)

∴ (p, -q) = (-6, 15)

⇒ p = -6 and -q = 15

⇒ p = -6 and q = -15

⇒ 2p + 3q = 2(-6) + 3(-15)

= -12 - 45

= -57.

Hence, Option 1 is the correct option.

If the point A(m, n) is first reflected in the x-axis and then reflected in the y-axis to the point A"(-12, -18), then the value of (2m - n) is :

1. 6

2. -6

3. -30

4. 30

Answer

Given, point A(m, n).

On reflection in x-axis, the sign of y-coordinate changes,

(m, n) ⇒ (m, -n)

On reflection in y-axis, the sign of x-coordinate changes,

(m, -n) ⇒ (-m, -n).

Given,

Final coordinates = A"(-12, -18)

∴ (-m, -n) = (-12, -18)

⇒ -m = -12 and -n = -18

⇒ m = 12 and n = 18

⇒ 2m - n = 2(12) - 18

⇒ 24 - 18

⇒ 6.

Hence, Option 1 is the correct option.

If the point A(m, n) is first reflected in the y-axis and then reflected in the x-axis to the point A"(-10, 15), then the value of (m - n) is :

1. -25

2. -5

3. 5

4. 25

Answer

Given, point A(m, n).

On reflection in y-axis, the sign of x-coordinate changes,

(m, n) ⇒ (-m, n)

On reflection in x-axis, the sign of y-coordinate changes,

(-m, n) ⇒ (-m, -n).

Given,

Final coordinates = A"(-10, 15)

∴ (-m, -n) = (-10, 15)

⇒ -m = -10 and -n = 15

⇒ m = 10 and n = -15

⇒ (m - n) = 10 - (-15) = 25.

Hence, Option 4 is the correct option.