Question

posttest: transformations on the coordinate plane
the triangle is dilated with a scale factor of 3 with its center of dilation at the origin. what is the length of the longest side of the resulting triangle?
12 units
2 units
18 units
6 units

Explanation:

Step1: Find original base length

The original triangle has vertices at (2,0), (8,0), and (5,-3). The base is between (2,0) and (8,0). Length = \(8 - 2 = 6\) units.

Step2: Apply dilation scale factor

Dilation scale factor is 3. New length = \(6\times3 = 18\) units. The other sides (the legs) are equal in original (distance from (2,0) to (5,-3): \(\sqrt{(5 - 2)^2+(-3 - 0)^2}=\sqrt{9 + 9}=\sqrt{18}\approx4.24\), same for (5,-3) to (8,0)). So base is longest original, scaled to 18.

Answer:

18 units (corresponding to the option "18 units")