Question

given q(-2, 0), r(4, -4), & s(2, 4), graph △qrs and △qrs based on the information below. 11. dilation about (3, 1), with a scale factor of 2

Explanation:

Step1: Recall dilation formula for point

For a point $(x,y)$ dilated about center $(h,k)$ with scale factor $k_s$, the new point $(x',y')$ is:
$$x' = h + k_s(x - h)$$
$$y' = k + k_s(y - k)$$
Here, $(h,k)=(3,1)$, $k_s=2$.

Step2: Calculate $Q'$ from $Q(-2,0)$

Substitute $x=-2,y=0$:
$$x' = 3 + 2(-2 - 3) = 3 + 2(-5) = 3 - 10 = -7$$
$$y' = 1 + 2(0 - 1) = 1 + 2(-1) = 1 - 2 = -1$$

Step3: Calculate $R'$ from $R(4,-4)$

Substitute $x=4,y=-4$:
$$x' = 3 + 2(4 - 3) = 3 + 2(1) = 3 + 2 = 5$$
$$y' = 1 + 2(-4 - 1) = 1 + 2(-5) = 1 - 10 = -9$$

Step4: Calculate $S'$ from $S(2,4)$

Substitute $x=2,y=4$:
$$x' = 3 + 2(2 - 3) = 3 + 2(-1) = 3 - 2 = 1$$
$$y' = 1 + 2(4 - 1) = 1 + 2(3) = 1 + 6 = 7$$

Answer:

$Q'(-7, -1)$
$R'(5, -9)$
$S'(1, 7)$

(To graph: Plot original points $Q(-2,0)$, $R(4,-4)$, $S(2,4)$ and connect to form $\triangle QRS$. Then plot the calculated $Q'$, $R'$, $S'$ and connect to form $\triangle Q'R'S'$.)