What is the image point of (8,-1) after the transformation D_{4}\circ R_{180^{\circ}}?

Answer 1

To find the image point, apply the transformations in order (right to left):

Step 1: R₁₈₀° (Rotation 180° about origin)

Rotation by 180° maps (x, y) → (-x, -y)

(8, -1) → (-8, 1)

Step 2: D₄ (Dilation by scale factor 4)

Dilation by factor 4 maps (x, y) → (4x, 4y)

(-8, 1) → (-32, 4)

Answer: (-32, 4)