Question

practice 8.2.02 christian lopez problem 6 here are points a and b. point f is the image of point a using point b as the center of dilation and a scale factor of 1/2. drag the moveable point to plot point f.

Explanation:

Step1: Recall dilation formula

If we have a center of dilation $B(x_B,y_B)$, a point $A(x_A,y_A)$ and a scale - factor $k$, the coordinates of the dilated point $F(x_F,y_F)$ are given by the formula $x_F=x_B + k(x_A - x_B)$ and $y_F=y_B + k(y_A - y_B)$. Here $k=\frac{1}{2}$.

Step2: Calculate $x$ - coordinate of $F$

Let $A=(x_A,y_A)$ and $B=(x_B,y_B)$. Then $x_F=x_B+\frac{1}{2}(x_A - x_B)=\frac{x_A + x_B}{2}$. This means that point $F$ lies on the line segment $\overline{BA}$ and is the mid - point between $B$ and $A$.

Step3: Calculate $y$ - coordinate of $F$

Similarly, $y_F=y_B+\frac{1}{2}(y_A - y_B)=\frac{y_A + y_B}{2}$.
To plot point $F$: Draw a line segment connecting points $A$ and $B$. Then find the mid - point of the line segment $\overline{BA}$. That mid - point is point $F$.

Answer:

Plot the mid - point of the line segment connecting $A$ and $B$ as point $F$.