Question

If triangle F'G'H' is a dilation of triangle FGH with a scale factor of 3, what are the values of X and Y?

(a) X = 1, Y = 1
(b) X = 3, Y = 3
(c) X = 1, Y = 3
(d) X = 3, Y = 1

Answer 1

The values of X and Y in triangle F'G'H' are X = 3 and Y = 3.

Step-by-step explanation:

To find the values of X and Y, we need to understand how dilation works. Dilation is a transformation that changes the size of a figure without changing its shape. In this case, triangle F'G'H' is a dilation of triangle FGH with a scale factor of 3.

When you dilate a figure with a scale factor of 3, every side of the figure becomes 3 times longer. So, if the length of side FG in triangle FGH is X, then the length of side F'G' in triangle F'G'H' is 3X. Similarly, if the length of side GH in triangle FGH is Y, then the length of side G'H' in triangle F'G'H' is 3Y.

Therefore, the values of X and Y are X = 3 and Y = 3. So, the correct answer is (b) X = 3, Y = 3.