Question

In the following figure, the smaller triangle is the image of the larger triangleunder a dilation centered at point O. Find the scale factor and the length of x andy as pictured.

Answer 1

scale factor: 3/5

x = 9

y = 7.2

Step-by-step explanation:

The smaller triangle is an image of the larger triangle.

The scale factor is the ratio of the corresponding side lengths of the smaller triangle and the larger triangle.

Now from the diagram we see that when the one side length of the image is 6 then the length of the corresponding side for the larger triangle is 10 units. Therefore, the scale factor is

`(6)/(10)`

which as a simplified fraction is to give

`(3)/(5)`

Now to find the value of x, we just multiply the corresponding side length of the bigger triangle by the scale factor. Hence,

`x=15*(3)/(5)`

which simplifies to give

`x=9`

Similarly, the measure of side length y is

`y=12*(3)/(5)=7.2`

Hence, to summerise

scale factor: 3/5

x = 9

y = 7.2