Question

triangle abc will be dilated according to the rule $d_{f,0.25}(x,y)$, where point f is the center of dilation. what will be the coordinates of vertex a of the image? $\bigcirc$ $(-8,-4)$ $\bigcirc$ $(-2,-1)$ $\bigcirc$ $(0,0)$ $\bigcirc$ $(1,0)$

Explanation:

Step1: Identify key coordinates

From the graph:

• Coordinates of $A$: $(-4, -3)$
• Coordinates of center $F$: $(3, 1)$

Step2: Apply dilation formula

The dilation rule $D_{F,0.25}(x,y)$ uses the formula:
$$(x', y') = (F_x + 0.25(x - F_x), F_y + 0.25(y - F_y))$$
Substitute $x=-4, y=-3, F_x=3, F_y=1$:
$$x' = 3 + 0.25(-4 - 3) = 3 + 0.25(-7) = 3 - 1.75 = 1.25$$
$$y' = 1 + 0.25(-3 - 1) = 1 + 0.25(-4) = 1 - 1 = 0$$

Note: Correcting for potential graph interpretation error (if $A$ is $(-4,-4)$ instead):
$$x' = 3 + 0.25(-4 - 3) = 3 - 1.75 = 1.25$$
$$y' = 1 + 0.25(-4 - 1) = 1 - 1.25 = -0.25$$
The closest matching option is $(1,0)$.

Answer:

(1, 0)