Question

figure ( y ) is the result of a transformation on figure ( x ). which transformation would accomplish this?

answer
a rotation ( 90^circ ) counterclockwise about the origin
a translation 5 units left and 3 units down
a translation 3 units right and 5 units up
a rotation ( 90^circ ) clockwise about the origin

Explanation:

First, identify key vertices of Figure X: for example, (4,0), (2,0), (4,-3). Test each transformation:

1. For a 90° counterclockwise rotation about the origin, the rule is $(x,y) \to (-y,x)$. Applying this to (4,0): $(0,4)$; (2,0): $(0,2)$; (4,-3): $(3,4)$ — this does not match Figure Y's vertices.
2. For translation 5 left, 3 down: $(x,y) \to (x-5,y-3)$. Applying to (4,0): $(-1,-3)$; (2,0): $(-3,-3)$; (4,-3): $(-1,-6)$ — these match the vertices of Figure Y.
3. Translation 3 right, 5 up would move the figure away from Figure Y's position, so it is incorrect.
4. 90° clockwise rotation rule is $(x,y) \to (y,-x)$. Applying to (4,0): $(0,-4)$; (2,0): $(0,-2)$; (4,-3): $(-3,-4)$ — this does not match Figure Y.

Answer:

A translation 5 units left and 3 units down