Question

Consider the rectangle.

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.