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? $(-8,-4)$ $(-2,-1)$ $(0,0)$ $(1,0)$

Explanation:

Step1: Determine the distance from point A to center F

From the graph, point \(A(-4,-4)\) and center \(F(3,1)\). The horizontal distance \(x = 3-(-4)=7\), vertical distance \(y = 1 - (-4)=5\).

Step2: Apply the dilation rule

The dilation rule \(D_{F,0.25}(x,y)\) means we multiply the distance from the center by \(0.25\). New horizontal distance \(7\times0.25 = 1.75\), new vertical distance \(5\times0.25=1.25\). But another way: formula for dilation \((x,y)\to(0.25(x - 3)+3,0.25(y - 1)+1)\) (using center \(F(3,1)\)). For \(A(-4,-4)\), \(x'=0.25(-4 - 3)+3=0.25\times(-7)+3=-1.75 + 3 = 1\), \(y'=0.25(-4 - 1)+1=0.25\times(-5)+1=-1.25 + 1=0\)

Answer:

\((1,0)\)