Question

Use the image to answer the question.

A coordinate plane's x-axis ranges from negative 1 to 8 and its y-axis ranges from negative 2 to 5, both by 1-unit increments. 3 points forming a triangle are plotted, labeled upper X, upper Y, and upper Z, respectively.
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If you dilate triangle XYZ
to form X′Y′Z′
using a magnitude of 2 and a center of dilation at (2,0)
, what are the coordinates of the dilated triangle?

(1 point)
Responses

X′(2,8)
, Y′(10,0)
, Z′(12,4)
upper X prime left parenthesis 2 comma 8 right parenthesis , upper Y prime left parenthesis 10 comma 0 right parenthesis , upper Z prime left parenthesis 12 comma 4 right parenthesis

X′(6,4)
, Y′(10,0)
, Z′(11,4)
upper X prime left parenthesis 6 comma 4 right parenthesis , upper Y prime left parenthesis 10 comma 0 right parenthesis , upper Z prime left parenthesis 11 comma 4 right parenthesis

X′(2,2)
, Y′(4,0)
, Z′(4.5,1)
upper X prime left parenthesis 2 comma 2 right parenthesis , upper Y prime left parenthesis 4 comma 0 right parenthesis , upper Z prime left parenthesis 4.5 comma 2 right parenthesis

X′(2,6)
, Y′(8,0)
, Z′(9.5,3)

Answer 1

X'(2, 8), Y'(10, 0), Z'(12, 4)

Work: For center C=(2,0) and scale k=2, P' = C + 2(P − C). Applying to X(2,4), Y(6,0), Z(7,2) gives X'=(2,8), Y'=(10,0), Z'=(12,4).