Question

What transformation transforms (p, q) to (q, p)​?

A: a reflection over the x-axis
B:a reflection over the y-axis
C:a reflection over y = x
D:a rotation of 90° about the origin

Answer 1

A reflection over the y=x, will transform (p, q) to (q, p)​

Solution-

A reflection over the x-axis

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite (sign is changed).

The point (x, y) becomes (x, -y)

A reflection over the y-axis

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (sign is changed).

The point (x, y) becomes (-x, y)

A reflection over y = x

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places (sign remains as it is).

The point (x, y) becomes (y, x)

A rotation of 90° about the origin

Rotation of point (x, y) about the origin O through 90° in clockwise direction, the new position will be (y, -x).

Rotation of point (x, y) about the origin O through 90° in counter-clockwise direction, the new position will be (-y, x).

Therefore, option C is correct.

Answer 2

we are given the two points (p,q) and (q,p) and we are asked in the problem to determine the transformation that happened between points. In this case, the the reflection cannot be over x axis nor y axis but over the line y = x. The answer then is C