Question

Point Q of quadrilateral QRST is (-9,2). What is the image of Q after QRST has been reflected across

the y-axis and then rotated 90 degrees about the origin?
• (2,-2).
• (-29)
(9,2)
None of the other answers are correct
• (-9,-2)

Answer 1

The image of Q after QRST has been reflected across the y-axis and then rotated 90 degrees about the origin is (-2,9 ), (2,-9) is correct .

The point Q(-9,2) undergoes a reflection across the y-axis, resulting in Q'(9,2).

Subsequently, two possible 90-degree rotations about the origin are considered.

For a counterclockwise rotation, the coordinates become Q'(-2,9), while for a clockwise rotation, the coordinates become Q'(2,-9).

The process of reflection across the y-axis involves negating the x-coordinate, and the rule for this transformation is (x, y) → (-x, y).

Applied to Q(-9,2), it yields Q'(9,2).

For a counterclockwise rotation of 90 degrees, the rule is (x, y) → (-y, x). Applying this to the reflected point Q'(9,2) results in Q'(-2,9).

Alternatively, for a clockwise rotation of 90 degrees, the rule is (x, y) → (y, -x). Applying this rule to the reflected point Q'(9,2) yields Q'(2,-9).

Therefore, after a reflection across the y-axis followed by a 90-degree rotation (either counterclockwise or clockwise) about the origin, the coordinates of the final image point Q' can be either (-2,9) or (2,-9), depending on the direction of rotation.

Answer 2

(-2,9)

(2,-9)

Explanation:

The point Q of quadrilateral QRST has coordinate (-9,2).

When this point is reflected across the y-axis , we negate the x-coordinate to obtain
`(--9,2)=(9,2)`.

This point is again rotated through an angle of 90 degrees(counterclockwise) about the origin.

The rule for 90 degrees counterclockwise rotation is
`(x,y)\to(-y,x)`.

`\implies (9,2)\to(-2,9)`

Therefore the image of Q(-9,2) after a reflection across the y-axis followed by a 90 degrees counterclockwise rotation about the origin is is Q'(-2,9).

However, the rotation could also be clockwise.

The rule for 90 degrees clockwise rotation is
`(x,y)\to(y,-x)`.

`\implies (9,2)\to(2,-9)`

The image of Q(-9,2) after a reflection across the y-axis followed by a 90 degrees clockwise rotation about the origin is is Q'(2,-9).

Both answers are there, so you can check them since the question did not specify the direction.