Question

rotate the figure 270° around (-1, 3). a(2, 1) b(5, 1) c(8, -4)

Explanation:

Step1: Recall rotation formula

The formula for rotating a point $(x,y)$ counter - clockwise about a center $(a,b)$ by an angle $\theta$ is given by:
$x'=(x - a)\cos\theta-(y - b)\sin\theta+a$ and $y'=(x - a)\sin\theta+(y - b)\cos\theta+b$. Here $\theta = 270^{\circ}$, $\cos270^{\circ}=0$, $\sin270^{\circ}=- 1$, $a=-1$, $b = 3$.

Step2: Rotate point A$(2,1)$

For point A$(x = 2,y = 1)$:
$x'=(2+1)\times0-(1 - 3)\times(-1)-1=-3$
$y'=(2 + 1)\times(-1)+(1 - 3)\times0+3=0$
So the new point A' is $(-3,0)$.

Step3: Rotate point B$(5,1)$

For point B$(x = 5,y = 1)$:
$x'=(5 + 1)\times0-(1 - 3)\times(-1)-1=-3$
$y'=(5 + 1)\times(-1)+(1 - 3)\times0+3=-3$
So the new point B' is $(-3,-3)$.

Step4: Rotate point C$(8,-4)$

For point C$(x = 8,y=-4)$:
$x'=(8 + 1)\times0-(-4 - 3)\times(-1)-1=-8$
$y'=(8 + 1)\times(-1)+(-4 - 3)\times0+3=-6$
So the new point C' is $(-8,-6)$.

Answer:

A'$(-3,0)$, B'$(-3,-3)$, C'$(-8,-6)$