Question

1. triangle uvw and triangle pqr are transformed on a coordinate plane. complete each rule with the coordinates of the image of the transformation. move the correct answer into each box in the table. each answer may be used more than once. not all answers will be used. (-x, -y) (y, -x) (-x, y) (x, -y) transformation rule triangle uvw reflected across the y-axis (x, y) → triangle pqr rotated 90° clockwise about the origin (x, y) →

Explanation:

Step1: Reflect across y - axis rule

When a point \((x,y)\) is reflected across the \(y\) - axis, the \(y\) - coordinate remains the same and the \(x\) - coordinate changes its sign. So the transformation rule is \((x,y)\to(-x,y)\).

Step2: Rotate \(90^{\circ}\) clockwise rule

The rule for rotating a point \((x,y)\) \(90^{\circ}\) clockwise about the origin is to swap the \(x\) and \(y\) coordinates and then change the sign of the new \(x\) - coordinate (or equivalently, \((x,y)\to(y, - x)\)).

Answer:

For "Triangle \(UVW\) reflected across the \(y\) - axis", the rule is \((x,y)\to\boldsymbol{(-x,y)}\).
For "Triangle \(PQR\) rotated \(90^{\circ}\) clockwise about the origin", the rule is \((x,y)\to\boldsymbol{(y, - x)}\).