Question

which single transformation maps figure tuvw onto its image? rotate 90° counterclockwise around the origin. reflect across the y - axis. translate 4 units to the right.

Explanation:

Step1: Analyze coordinate - change rule

For a point $(x,y)$ reflected across the $y$-axis, the new coordinates are $(-x,y)$. In the given table, for point $T(-5, - 1)$, its image $T'(5,-1)$; for $U(-2,-1)$, its image $U'(2,-1)$; for $V(-2,-3)$, its image $V'(2,-3)$; for $W(-5,-4)$, its image $W'(5,-4)$. The $x$-coordinates change sign and the $y$-coordinates remain the same, which is the rule for reflection across the $y$-axis.

Step2: Check other transformation rules

A $90^{\circ}$ counter - clockwise rotation around the origin changes the coordinates of a point $(x,y)$ to $(-y,x)$, which is not the case here. A translation 4 units to the right changes the $x$-coordinate of a point $(x,y)$ to $x + 4$, and this also does not match the given coordinate changes.

Answer:

Reflect across the $y$-axis.