Question

dig deeper △abc has vertices a(4, 2), b(4, 6), and c(7, 2). find the coordinates of the vertices of the image after a dilation with center (4, 0) and scale factor 2. coordinates: a (□, □), b (□, □), and c (□, □)

Explanation:

Step1: Recall the dilation formula

For a dilation with center \((h,k)\) and scale factor \(s\), the coordinates of a point \((x,y)\) after dilation \((x',y')\) are given by:
\(x' = h + s(x - h)\)
\(y' = k + s(y - k)\)

Step2: Find \(A'\)

Given \(A(4,2)\), center \((4,0)\), scale factor \(s = 2\)
\(x' = 4+2(4 - 4)=4+2(0)=4\)
\(y' = 0+2(2 - 0)=0 + 4 = 4\)
So \(A'(4,4)\)

Step3: Find \(B'\)

Given \(B(4,6)\), center \((4,0)\), scale factor \(s = 2\)
\(x' = 4+2(4 - 4)=4+0 = 4\)
\(y' = 0+2(6 - 0)=0+12 = 12\)
So \(B'(4,12)\)

Step4: Find \(C'\)

Given \(C(7,2)\), center \((4,0)\), scale factor \(s = 2\)
\(x' = 4+2(7 - 4)=4+2(3)=4 + 6 = 10\)
\(y' = 0+2(2 - 0)=0 + 4 = 4\)
So \(C'(10,4)\)

Answer:

\(A'(4,4)\), \(B'(4,12)\), \(C'(10,4)\)