Question

1. square abcd with vertices a(-7, 5), b(-4, 7), c(-2, 4), and d(-5, 2): 90° counterclockwise
2. triangle def with

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$.

Step2: Apply rule to point A

For point $A(-7,5)$, using the rule $(x,y)\to(-y,x)$, we have $x=-7,y = 5$. Then $A'=(-5,-7)$.

Step3: Apply rule to point B

For point $B(-4,7)$, with $x=-4,y = 7$, then $B'=(-7,-4)$.

Step4: Apply rule to point C

For point $C(-2,4)$, with $x=-2,y = 4$, then $C'=(-4,-2)$.

Step5: Apply rule to point D

For point $D(-5,2)$, with $x=-5,y = 2$, then $D'=(-2,-5)$.

Answer:

$A'(-5,-7), B'(-7,-4), C'(-4,-2), D'(-2,-5)$