Question

the coordinates of the vertices of a quadrilateral are e (-2, 5), f (-2, 6), g (-3, 6), and h (-5, 5). quadrilateral efgh is rotated 270° clockwise with the origin as the center of rotation to create quadrilateral efgh. which graph correctly shows quadrilateral efgh?

Explanation:

Step1: Recall rotation rule

A 270 - clockwise rotation about the origin has the rule $(x,y)\to(y, - x)$.

Step2: Apply rule to point E

For point E(-2,5), after rotation, $x=-2,y = 5$, so $E'=(5,2)$.

Step3: Apply rule to point F

For point F(-2,6), after rotation, $x=-2,y = 6$, so $F'=(6,2)$.

Step4: Apply rule to point G

For point G(-3,6), after rotation, $x=-3,y = 6$, so $G'=(6,3)$.

Step5: Apply rule to point H

For point H(-5,5), after rotation, $x=-5,y = 5$, so $H'=(5,5)$.

Answer:

We need to check which of the given graphs has the points E'(5,2), F'(6,2), G'(6,3) and H'(5,5). Without seeing the full - set of answer choices in a way that we can directly pick one, the process to find the correct graph is to plot these new points on a coordinate plane and match with the given graphs.