Question

Triangle XYZ
is drawn on a coordinate plane with vertices X(0,4)
, Y(2,0)
, and Z(4,7)
. If you dilate the triangle to form triangle X′Y′Z′
using a magnitude of 12
and a center of dilation at (4,7)
, what are the coordinate points of the new vertices?(1 point)
Responses

X′(−4,1)
, Y′(0,−7)
, Z′(4,7)
upper X prime left parenthesis negative 4 comma 1 right parenthesis , upper Y prime left parenthesis 0 comma negative 7 right parenthesis , upper Z prime left parenthesis 4 comma 7 right parenthesis

X′(4,11)
, Y′(6,7)
, Z′(8,14)
upper X prime left parenthesis negative 4 comma 11 right parenthesis , upper Y prime left parenthesis 6 comma 7 right parenthesis , upper Z prime left parenthesis 8 comma 14 right parenthesis

X′(2,5.5)
, Y′(3,3.5)
, Z′(4,7)
upper X prime left parenthesis 2 comma 5.5 right parenthesis , upper Y prime left parenthesis 3 comma 3.5 right parenthesis , upper Z prime left parenthesis 4 comma 7 right parenthesis

X′(−4,−3)
, Y′(−2,−7)
, Z′(0,0)
upper X prime left parenthesis negative 4 comma negative 3 right parenthesis , upper Y prime left parenthesis negative 2 comma negative 7 right parenthesis , upper Z prime left parenthesis 0 comma 0 right parenthesis
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Answer 1

Use P' = C + k(P − C) with center C = (4,7).

For k = 12:
- X' = (4 + 12*(0−4), 7 + 12*(4−7)) = (4 − 48, 7 − 36) = (−44, −29)
- Y' = (4 + 12*(2−4), 7 + 12*(0−7)) = (4 − 24, 7 − 84) = (−20, −77)
- Z' = (4 + 12*(4−4), 7 + 12*(7−7)) = (4, 7)

So the image is X'(−44, −29), Y'(−20, −77), Z'(4, 7) — none of the given choices match.

If the problem actually meant a scale factor of 1/2 (often written 1/2 but sometimes misprinted as "12"), then the correct choice is X'(2, 5.5), Y'(3, 3.5), Z'(4, 7) (the third option).