Question

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

Explanation:

Step1: Recall reflection rule

For a reflection over the x - axis, the rule is $(x,y)\to(x, - y)$.

Step2: Check vertices

For Figure A with vertices, when reflected over x - axis using $(x,y)\to(x, - y)$, it matches Figure B. For example, if a vertex of A is $(x_1,y_1)$, after reflection over x - axis, it becomes $(x_1,-y_1)$ which is the corresponding vertex in B.

Step3: Eliminate other options

A $90^{\circ}$ counter - clockwise rotation about origin has rule $(x,y)\to(-y,x)$ and a $270^{\circ}$ counter - clockwise rotation has rule $(x,y)\to(y, - x)$. A reflection over y - axis has rule $(x,y)\to(-x,y)$. These do not match the transformation from A to B.

Answer:

A. A reflection over the x - axis