Question

problem 3
here are points a and b.
point f is the image of point b using point a as the center of dilation and a scale factor of $\frac{1}{3}$.
drag the moveable point to plot f.

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 $k = \frac{1}{3}$, the coordinates of the dilated point $F=(x_f,y_f)$ are given by the formula $x_f=x_a + k(x_b - x_a)$ and $y_f=y_a + k(y_b - y_a)$.

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

Let $A=(x_a,y_a)$ and $B=(x_b,y_b)$. Then $x_f=x_a+\frac{1}{3}(x_b - x_a)=\frac{2x_a + x_b}{3}$.

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

$y_f=y_a+\frac{1}{3}(y_b - y_a)=\frac{2y_a + y_b}{3}$.

Step4: Plot the point

Using the calculated coordinates $(x_f,y_f)$, plot the point $F$.

Since no specific coordinates of $A$ and $B$ are given in the text (but the process to find the coordinates of $F$ is shown above), if we assume $A$ and $B$ are on a coordinate - plane, we would use the above - derived coordinate formulas to find the location of $F$ relative to $A$ and $B$.

Answer:

Plot the point $F$ using the coordinate formulas $x_f=\frac{2x_a + x_b}{3}$ and $y_f=\frac{2y_a + y_b}{3}$ where $(x_a,y_a)$ are the coordinates of $A$ and $(x_b,y_b)$ are the coordinates of $B$.