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Triangle ABC has coordinates of A(–8, –8), B(4, –2), and C(2, 2). Find the coordinates of its image after a dilation centered at the origin with a scale factor of 1.5.

A) A(–5.33, –5.33), B(2.67, –1.33), C(1.33, 1.33)
B) A(–8, –8), B(4, –2), C(2, 2)
C) A(–12, –12), B(6, –3), C(3, 3)
D) A(–12, –8), B(6, –2), C(3, 2)

User Hugolpz
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2 Answers

2 votes
the answer is (C) because you multiply each point by 1.5.
User Neeraj Shukla
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7.3k points
1 vote

Answer:

Option C -A(–12, –12), B(6, –3), C(3, 3)

Explanation:

Given : Triangle ABC has coordinates of A(–8, –8), B(4, –2), and C(2, 2).

To find : The coordinates of its image after a dilation centered at the origin with a scale factor of 1.5.?

Solution :

A dilation centered at the origin with a scale factor of +k.

Coordinates became,
A(x,y)=A'(kx,ky)

We have given k=1.5

And coordinates A(-8,8), B (4, -2), C (2,2)


A(-8,8)=A'(1.5(-8),1.5(8))=A'(-12,12)


B(4,-2)=B'(1.5(4),1.5(-2))=B'(6,-3)


C(2,2)=C'(1.5(2),1.5(2))=C'(3,3)

Therefore, The new coordinates after dilation is A(–12, –12), B(6, –3), C(3, 3)

Hence, Option C is correct.

User Steampowered
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