Question

Consider the rectangle.

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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)

Answer 1

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.