Mathematics
The point P(3, 4) is reflected in the line y = x to point (a, b). Then:
a = b
ab = 1
b - a = 1
none of these
Answer
When a point (x, y) is reflected across the line y = x, the coordinates are swapped, resulting in the point (y, x).
Therefore, the reflection of P(3, 4) is (4, 3). So, a = 4 and b = 3.
Checking all the given options :
Option 1. a = b ⇒ 4 ≠ 3, which is false.
Option 2. ab = 1 ⇒ 4 x 3 = 12 ≠ 1, which is false.
Option 3. b - a = 1 ⇒ 3 - 4 = -1 ≠ 1, which is false.
Hence, option 4 is the correct option.
Related Questions
Point (5, 6) is reflected in a line to get the point (-5, 6). The line of reflection is :
x-axis
x = 5
y = 0
y-axis
(i) Point A is reflected in y-axis to get point B.
(ii) Point B is reflected in origin to get point C.
(iii) Point C is reflected in y = 0 to get point P. Now, which of the following coincides with point P.
Point A
Point B
Points B and C
Points A and B
The point P(5, 7) is reflected to P' in x-axis and O' is the image of O (origin) in the line PP'. The co-ordinates of O' are :
(10, 0)
(0, 10)
(10, 10)
(5, 5)
The point P is reflected in x = 0 to get the point P' and the point P' is reflected in y = 0 to get the point P". Which two points out of P, P' and P" are invariant under this reflection.
P" = P
P" = P'
P' = P
no-one