Question

1. quadrilateral abcd with vertices a(4, 0), b(6, -2), c(8, -7), and d(0, -5): 270° counterclockwise about the origin a(_, _) b(_, _) c(_, _) d(_, _)

Explanation:

Step1: Recall rotation rule

The rule for a 270 - counter - clockwise rotation about the origin is $(x,y)\to(y, - x)$.

Step2: Rotate point A

For $A(4,0)$, using the rule $(x,y)\to(y, - x)$, we substitute $x = 4$ and $y = 0$. So $A'(0,-4)$.

Step3: Rotate point B

For $B(6,-2)$, substitute $x = 6$ and $y=-2$ into the rule. We get $B'(-2,-6)$.

Step4: Rotate point C

For $C(8,-7)$, substitute $x = 8$ and $y=-7$ into the rule. We have $C'(-7,-8)$.

Step5: Rotate point D

For $D(0,-5)$, substitute $x = 0$ and $y=-5$ into the rule. We obtain $D'(-5,0)$.

Answer:

$A'(0,-4)$
$B'(-2,-6)$
$C'(-7,-8)$
$D'(-5,0)$