Question

practice 8.2.02 christian lopez problem 5 here are points a and b. point e is the image of point b using point a as the center of dilation and a scale factor of 1/2. drag the moveable point to plot point e.

Explanation:

Step1: Recall dilation formula

If point $A=(x_a,y_a)$ is the center of dilation and point $B=(x_b,y_b)$ is being dilated with scale - factor $k = \frac{1}{2}$, the coordinates of the dilated point $E=(x_e,y_e)$ are given by the formula $x_e=x_a + k(x_b - x_a)$ and $y_e=y_a + k(y_b - y_a)$.

Step2: Simplify the formula

$x_e=x_a+\frac{1}{2}(x_b - x_a)=\frac{2x_a+x_b - x_a}{2}=\frac{x_a + x_b}{2}$, and $y_e=y_a+\frac{1}{2}(y_b - y_a)=\frac{2y_a+y_b - y_a}{2}=\frac{y_a + y_b}{2}$. Geometrically, point $E$ is the mid - point of the line segment joining $A$ and $B$. So, to plot point $E$, draw a line segment connecting points $A$ and $B$, and then find the mid - point of this line segment. That mid - point is point $E$.

Answer:

Plot the mid - point of the line segment joining points $A$ and $B$ as point $E$.