Question

Triangle QRS has coordinates Q(-2, -2), R(0, 3), and S(4, -2) and is dilated by a scale factor of 2. Determine the new coordinates of point S', and state whether the dilation is an enlargement or a reduction

Answer 1

Given:

Triangle QRS has coordinates Q(-2, -2), R(0, 3), and S(4, -2) and is dilated by a scale factor of 2.

To find:

The new coordinates of point S', and state whether the dilation is an enlargement or a reduction.

Solution:

If a figure is dilated by factor k with origin as center of dilation, then

$(x,y)\to (kx,ky)$

Where, 0<k<1 is reduction and k>1 is enlargement.

The figure is dilated by scale factor 2 which is greater than 1, so the dilation is an enlargement. The rule of dilation is:

$(x,y)\to (2x,2y)$

Using this rule, we get

$S(4,-2)\to S'(2(4),2(-2))$

$S(4,-2)\to S'(8,-4)$

Therefore, the new coordinates of point S' are (8,-4).