Question

card 11
a choose a center of dilation and label it point p.
b dilate triangle fgh using a scale factor of 1/2.

Explanation:

Step1: Choose a center of dilation

Let's choose the origin $(0,0)$ as the center of dilation $P$. This is a common - choice for simplicity in coordinate - based dilations.

Step2: Recall the dilation formula

If the center of dilation is the origin $(0,0)$ and the scale factor is $k$, for a point $(x,y)$ in the original figure, the coordinates of the dilated point $(x',y')$ are given by $(x',y')=(k\cdot x,k\cdot y)$. Here, $k = \frac{1}{2}$.
Suppose the coordinates of the vertices of $\triangle FGH$ are $F(x_1,y_1)$, $G(x_2,y_2)$, and $H(x_3,y_3)$.
For vertex $F$: If $F(x_1,y_1)$, then the dilated vertex $F'(x_1',y_1')=(\frac{1}{2}x_1,\frac{1}{2}y_1)$.
For vertex $G$: If $G(x_2,y_2)$, then the dilated vertex $G'(x_2',y_2')=(\frac{1}{2}x_2,\frac{1}{2}y_2)$.
For vertex $H$: If $H(x_3,y_3)$, then the dilated vertex $H'(x_3',y_3')=(\frac{1}{2}x_3,\frac{1}{2}y_3)$.
We would then plot the new triangle $\triangle F'G'H'$ with these dilated vertices on the coordinate - plane.

Answer:

a. Center of dilation $P=(0,0)$ (choice can vary, here we choose the origin).
b. Dilate each vertex of $\triangle FGH$ using the formula $(x',y') = (\frac{1}{2}x,\frac{1}{2}y)$ where $(x,y)$ are the coordinates of the original vertex and $(x',y')$ are the coordinates of the dilated vertex, then plot the new triangle.