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Consider the rectangle.

-
Which points could be the vertices of the image of the rectangle after it is dilated from the origin by a scale factor of 3? Select all that apply.
(0,5)
(0, 12)
(6,9)
(6,0)
(9, 4)
(9, 12)

Consider the rectangle. - Which points could be the vertices of the image of the rectangle-example-1
User IYoung
by
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1 Answer

5 votes

Given:

The graph of a rectangle.

The given rectangle is dilated from the origin by a scale factor of 3.

To find:

The vertices of the image of the rectangle after the dilation.

Solution:

From the given graph it is clear that the vertices of the rectangle are A(0,2), B(0,4), C(3,4) and D(3,2).

If a figure is dilated from the origin by a scale factor of 3, then


(x,y)\to (3x,3y)

Using this rule, the vertices of the image are:


A(0,2)\to A'(3(0),3(2))


A(0,2)\to A'(0,6)

Similarly,


B(0,4)\to B'(3(0),3(4))


B(0,4)\to B'(0,12)

And,


C(3,4)\to C'(3(3),3(4))


C(3,4)\to C'(9,12)

And,


D(3,2)\to D'(3(3),3(2))


D(3,2)\to D'(9,6)

The vertices of the image after dilation are (0,6), (0,12), (9,12), (9,6).

Therefore, the correct options are B and F.

User Haugholt
by
8.6k points

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