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Polygon ABCD with vertices at A(-4, 6), B(-2, 2), C(4,-2), D(4, 4) is dilated using a scale factor of to create polygon A'B'C'D'. Determine the vertices of polygon

4
A'B'C'D'.
OA(-3, 4.5), B(-1.5, 1.5), C(3, -1.5), D'(3, 3)
OA(-12, 18), B(-6, 6), C(12,-6), D'(12, 12)
OA(3, -4.5), B(1.5, -1.5), C(-3, 1.5), D'(-3,-3)
OA (4.5, -3), B(1.5, -1.5), C(-1.5, 3), D'(3, 3)

User Amitmula
by
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1 Answer

3 votes

Answer:

The correct answer is: OA(3, -4.5), B(1.5, -1.5), C(-3, 1.5), D'(-3,-3).

To dilate a point using a scale factor of 4, we multiply each coordinate of the original point by 4.

Thus, the coordinates of A' are (-4 * 4, 6 * 4) = (-16, 24)

The coordinates of B' are (-2 * 4, 2 * 4) = (-8, 8)

The coordinates of C' are (4 * 4, -2 * 4) = (16, -8)

The coordinates of D' are (4 * 4, 4 * 4) = (16, 16)

To check our work, we can plot these points on a graph and compare with the original polygon:

Original Polygon:

A(-4, 6) B(-2, 2)

* *

\ /

\ /

\ /

\ /

\ /

* *

C(4,-2) D(4,4)

Dilated Polygon:

A'(-16, 24) B'(-8, 8)

* *

\ /

\ /

\ /

*

C'(16,-8) D'(16,16)

If we divide the coordinates of the dilated polygon by 4, we get the answer:

A'(-16/4, 24/4) = (-4, 6)

B'(-8/4, 8/4) = (-2, 2)

C'(16/4, -8/4) = (4, -2)

D'(16/4, 16/4) = (4, 4)

So the vertices of polygon A'B'C'D' are OA (3, -4.5), B(1.5, -1.5), C(-3, 1.5), and D'(-3,-3).

User Joe Wu
by
8.8k points

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