Question

1. rectangle mnop with vertices m(-7, -2), n(-5, -1), o(-2, -7), and p(-4, -8): 90° counterclockwise about the origin

Explanation:

Step1: Recall the rotation rule

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

Step2: Rotate point M

For $M(-7,-2)$, applying the rule: $x=-7,y = - 2$. Then $x'=-(-2)=2$ and $y'=-7$. So $M'=(2,-7)$.

Step3: Rotate point N

For $N(-5,-1)$, with $x=-5,y=-1$. Then $x'=-(-1)=1$ and $y'=-5$. So $N'=(1,-5)$.

Step4: Rotate point O

For $O(-2,-7)$, where $x=-2,y = - 7$. Then $x'=-(-7)=7$ and $y'=-2$. So $O'=(7,-2)$.

Step5: Rotate point P

For $P(-4,-8)$, given $x=-4,y=-8$. Then $x'=-(-8)=8$ and $y'=-4$. So $P'=(8,-4)$.

Answer:

$M'(2,-7)$
$N'(1,-5)$
$O'(7,-2)$
$P'(8,-4)$