Question

which transformation would take figure a to figure b?
answer
a counterclockwise rotation of 270° about the origin
a counterclockwise rotation of 90° about the origin
a reflection over the x - axis
a reflection over the y - axis

Explanation:

Step1: Identify key points of Figure A

Let's take 3 vertices of Figure A: $(-8, -9)$, $(-8, -3)$, $(-3, -5)$

Step2: Apply 90° counterclockwise rotation rule

The rule for 90° counterclockwise rotation about the origin is $(x,y) \to (-y,x)$.

• For $(-8, -9)$: $(-(-9), -8) = (9, -8)$ → no, does not match Figure B.

Step3: Apply 270° counterclockwise rotation rule

The rule for 270° counterclockwise rotation (equivalent to 90° clockwise) about the origin is $(x,y) \to (y,-x)$.

• For $(-8, -9)$: $(-9, 8)$
• For $(-8, -3)$: $(-3, 8)$
• For $(-3, -5)$: $(-5, 3)$

These points match the vertices of Figure B.

Step4: Verify other options

• Reflection over x-axis: $(x,y) \to (x,-y)$: $(-8,-9) \to (-8,9)$, which does not match Figure B's points.
• Reflection over y-axis: $(x,y) \to (-x,y)$: $(-8,-9) \to (8,-9)$, which does not match Figure B's points.

Answer:

A counterclockwise rotation of 270° about the origin