Question

identify the transformation from b to d.
a) $90^circ$ clockwise rotation
b) $270^circ$ clockwise rotation
c) $180^circ$ rotation
d) $360^circ$ rotation

Explanation:

Step1: Define rotation rules

A 180° rotation (around origin) uses:
$$(x,y) \to (-x,-y)$$

Step2: Test triangle B vertices

Take vertex of B: $(-3,4)$. Apply rule:
$$(-3,4) \to (3,-4)$$
This matches a vertex of D. Repeat for other vertices of B: all map to D's vertices.

Step3: Eliminate other options

• 90° clockwise: $(x,y)\to(y,-x)$ does not match.
• 270° clockwise: $(x,y)\to(-y,x)$ does not match.
• 360° rotation: $(x,y)\to(x,y)$ (same shape, no match).

Answer:

c) 180° Rotation