Mathematics
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
Answer
Let co-ordinate of P be (x, y).
We know that,
On reflection in y-axis (x = 0), the sign of x-coordinate changes.
P(x, y) = P'(-x, y)
We know that,
On reflection in x-axis (y = 0), the sign of y-coordinate changes.
P'(-x, y) = P"(-x, -y)
No two points have same co-ordinate, there are no points that are invariant.
Hence, Option 4 is the correct option.
Related Questions
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)
Point A (4, -1) is reflected as A' in the y-axis. Point B on reflection in the x-axis is mapped as B' (-2, 5). Write the co-ordinates of A' and B.
The point P(x, y) is reflected in the line y = x to point P'(x', y'), then :
x = y
y' = x'
x = x' and y = y'
x = y' and y = x'
A triangle ABC is reflected in y-axis to get triangle A'B'C'. Triangle A'B'C' is reflected in line y = 0, to get △A"B"C". Then which of the following is not true ?
△A'B'C' ~ △A"B"C"
△A'B'C' ≅ △A"B"C"
△ABC ≅ △A"B"C"
△ABC ≠ △A"B"C"