Question

practice 8.2.02 christian lopez problem 3 here are points a and b. point c is the image of point b using point a as the center of dilation and a scale factor of 2. drag the moveable point to plot point c.

Explanation:

Step1: Recall dilation formula

If point $A(x_a,y_a)$ is the center of dilation, point $B(x_b,y_b)$ and the scale - factor is $k$, the coordinates of the dilated point $C(x_c,y_c)$ are given by $x_c=x_a + k(x_b - x_a)$ and $y_c=y_a + k(y_b - y_a)$. Here $k = 2$. Geometrically, we can also think of it as the vector from $A$ to $B$ being doubled.

Step2: Find the direction and distance

The vector from $A$ to $B$ is $\overrightarrow{AB}$. To find point $C$, we start at point $A$ and move in the direction of $\overrightarrow{AB}$ with a length that is twice the length of $\overrightarrow{AB}$.

Answer:

To plot point $C$, start at point $A$. Move in the direction from $A$ to $B$. The distance from $A$ to $C$ should be twice the distance from $A$ to $B$.