Mathematics
The point P(4, -7) on reflection in x-axis is mapped onto P'. Then P' on reflection in the y-axis is mapped onto P''. Find the coordinates of P' and P''. Write down a single transformation that maps P onto P''.
Answer
We know that,
Rule to find reflection of a point in x-axis :
- Retain the abscissa i.e. x-coordinate.
- Change the sign of ordinate i.e. y-coordinate.
∴ Coordinates of point P(4, -7) on reflection in x-axis is P'(4, 7).
We know that,
Rule to find reflection of a point in y-axis :
- Change the sign of abscissa i.e. x-coordinate.
- Retain the ordinate i.e. y-coordinate.
∴ Coordinates of point P'(4, 7) on reflection in y-axis is P''(-4, 7).
The single transformation that maps P(4, -7) onto P''(-4, 7) is reflection in the origin.
Related Questions
ABC is a triangle and its vertices A, B, C are reflected in y-axis to the points A', B' and C' respectively.
Assertion (A): Area (Δ ABC) = Area (Δ A'B'C').
Reason (R): The two triangles are congruent.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
A point is invariant with respect to both x-axis and y-axis.
Assertion (A): It is invariant with respect to origin also.
Reason (R): The point is origin itself.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
The point P(a, b) is first reflected in the origin and then reflected in the y-axis to P'. If P' has coordinates (3, -4), evaluate a, b.
A point P(a, b) become (-2, c) after reflection in the x-axis, and P becomes (d, 5) after reflection in the origin. Find the values of a, b, c and d.