Answered

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.

AA(–5.33, –5.33), B(2.67, –1.33), C(1.33, 1.33)
BA(–8, –8), B(4, –2), C(2, 2)
CA(–12, –12), B(6, –3), C(3, 3)
DA(–12, –8), B(6, –2), C(3, 2)

Verified Answer :

the answer is (C) because you multiply each point by 1.5.

Answer:

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

Step-by-step 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.

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