Question

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 $A(x_1,y_1)$ is the center of dilation and point $B(x_2,y_2)$ is the original - point with a scale factor $k$, the coordinates of the dilated point $C(x,y)$ are given by the formula $x=x_1 + k(x_2 - x_1)$ and $y=y_1 + k(y_2 - y_1)$. Here $k = 2$.

Step2: Geometric interpretation

In a geometric sense, we first find the vector $\overrightarrow{AB}$. Then, since the scale - factor is 2, the vector $\overrightarrow{AC}$ has the same direction as $\overrightarrow{AB}$ and is twice as long as $\overrightarrow{AB}$. Starting from point $A$, we move in the direction of $\overrightarrow{AB}$ and make the distance from $A$ to $C$ be twice the distance from $A$ to $B$.

Answer:

To plot point $C$, measure the distance from $A$ to $B$. Then, starting from point $A$, move in the same direction as from $A$ to $B$ and make the distance from $A$ to $C$ be twice the distance from $A$ to $B$.