Answered

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Dilate triangle ABC by a scale factor of 2 with a center of dilation of (2, 3). A(2, 5), B(-3, 3), C(2, -1)

Sagot :

Given the vertices of triangle ABC:

A(2, 5), B(-3, 3), C(2, -1)

Let's dilate the triangle ABC by a scale factor of 2 with a center of dilation of (2, 3)

Here, since we have a scale factor, k, of 2 and center of dilation (2, 3), apply the formula:

(x', y') = k(x - a)+a, k(y - b)+ b

Where:

(a, b) is the center of dilation: (2, 3)

(x, y) is the coordinate

(x' y') is the new coordinate

k is the sale factor = 2

Thus, we have the following:

A(2, 5) ==> 2(2 - 2)+2, 2(5 - 3)+3 ==> 2(0)+2, 2(2)+3 ==> (2, 9)

B(-3, 3) ==> 2(-3 - 2)+2, 2(3 - 3)+3 ==> 2(-5)+2, 2(0)+3 ==> (-8, 3)

C(2, -1) ==> 2(2 - 2)+2, 2(-1 - 3)+3 ==> 2(0)+2, 2(-4)+3 ==> (2, -5)

Therefore, the vertices of triangle ABC after the dilation are:

A'(2, 9), B'(-8, 3), C'(2, -5)

ANSWER:

A'(2, 9), B'(-8, 3), C'(2, -5)

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