Question

triangle abc has vertices a (8, 4), b (14, 16), and c (6, 10). what are the vertices of the image after a dilation with a scale factor of \\( \frac { 1 } { 2 } \\) using the origin as the center of dilation?
a = (__,) b = (,) c = (,__)
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Explanation:

Step1: Apply dilation formula

For a point \((x,y)\) dilated with scale factor \(k=\frac{1}{2}\) and center at origin \((0,0)\), the new point \((x',y')=(k\times x,k\times y)\)

Step2: Find \(A'\)

For \(A(8,4)\), \(x = 8,y = 4,k=\frac{1}{2}\)
\(x'=\frac{1}{2}\times8 = 4,y'=\frac{1}{2}\times4=2\)

Step3: Find \(B'\)

For \(B(14,16)\), \(x = 14,y = 16,k=\frac{1}{2}\)
\(x'=\frac{1}{2}\times14 = 7,y'=\frac{1}{2}\times16 = 8\)

Step4: Find \(C'\)

For \(C(6,10)\), \(x = 6,y = 10,k=\frac{1}{2}\)
\(x'=\frac{1}{2}\times6=3,y'=\frac{1}{2}\times10 = 5\)

Answer:

A' = (4, 2), B' = (7, 8), C' = (3, 5)