Question

guided instructions below to rotate the figure 90° counter - clockwise about the origin. fill out all of the corresponding points of the image figure. animate rotation again pre - image image (-5,1) → (-2,4) → (-2,8) → (-5,8) →

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 $(-5,1)$

For the point $(-5,1)$, substituting $x=-5$ and $y = 1$ into the rule $(-y,x)$, we get $(-1,-5)$.

Step3: Apply rule to $(-2,4)$

For the point $(-2,4)$, substituting $x=-2$ and $y = 4$ into the rule $(-y,x)$, we get $(-4,-2)$.

Step4: Apply rule to $(-2,8)$

For the point $(-2,8)$, substituting $x=-2$ and $y = 8$ into the rule $(-y,x)$, we get $(-8,-2)$.

Step5: Apply rule to $(-5,8)$

For the point $(-5,8)$, substituting $x=-5$ and $y = 8$ into the rule $(-y,x)$, we get $(-8,-5)$.

Answer:

$(-5,1)\to(-1,-5)$
$(-2,4)\to(-4,-2)$
$(-2,8)\to(-8,-2)$
$(-5,8)\to(-8,-5)$