Question

The larger triangle is a dilation of the smaller triangle find the values of x and y

Answer 1

So,

The scale factor in the dilation of a mathematical object determines how much larger or smaller the image will be (compared to the original object).

In this case, in the graph we can notice that the smaller side of the smaller triangle measures 2. The smaller side of the larger triangle measures 6. So the scale factor in the dilation of the triangle is 3 since the sides are three times larger.

Now, we can also use the fact that both triangles are similar triangles. Thus, the corresponding angles that they form are congruent and by the way equal. For this reason, we can equal the following expressions:

Therefore, y=25.

Now, to find the value of x we could state the following relationship using the scale factor of dilation:

Solving for x:

Therefore, x=5 and y=25.