Question

The vertices of the triangle are located as follows: upper X at left parenthesis 2 comma 4 right parenthesis, upper Y at left parenthesis 6 comma 0 right parenthesis, and upper Z at left parenthesis 7 comma 2 right parenthesis.

If you dilate triangle XYZ
𝑋
𝑌
𝑍
to form X′Y′Z′
𝑋
′
𝑌
′
𝑍
′
using a magnitude of 2 and a center of dilation at (2,0)
(
2
,
0
)
, what are the coordinates of the dilated triangle?

(1 point)
Responses

X′(2,8)
𝑋
′
(
2
,
8
)
, Y′(10,0)
𝑌
′
(
10
,
0
)
, Z′(12,4)
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)
𝑋
′
(
6
,
4
)
, Y′(10,0)
𝑌
′
(
10
,
0
)
, Z′(11,4)
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 pa

Answer 1

Use P' = C + 2(P − C) with center C = (2,0). So P' = (2 + 2(x−2), 2y) = (2x−2, 2y).

X(2,4) → X' = (2,8)
Y(6,0) → Y' = (10,0)
Z(7,2) → Z' = (12,4)

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