A triangle is dilated with the center of dilation at point U. Point E is a vertex of the triangle and point E′ is the corresponding vertex of the image. If UE = 2 centimeters and U′E′=10 centimeters, what is the scale factor?

A. −5.0
B. −0.2
C. 0.2
D. 5.0

the Answer is

D 5.0

scale factor = (new length) / (original length)

What are the coordinates of the image of point E after a dilation with center (0, 0) and scale factor of 1/3

Well, it seems like the triangle underwent some serious stretching! Let me calculate the scale factor for you.

The scale factor can be defined as the ratio of the corresponding lengths in the original and the image. In this case, the scale factor would be (U'E') / (UE).

So, let's plug in the given values: U'E' = 10 centimeters and UE = 2 centimeters.

Scale factor = (U'E') / (UE) = 10 / 2 = 5

Oh boy, that triangle got stretched by a factor of 5! So the correct answer is D. 5.0.

Remember, with great dilation power comes great responsibility!

To find the scale factor, we need to compare the corresponding side lengths of the original triangle and the dilated triangle.

In this case, we are given that the length of the side UE in the original triangle is 2 centimeters, and the length of the corresponding side U'E' in the dilated triangle is 10 centimeters.

The scale factor is the ratio of the lengths of the corresponding sides.

Scale factor = U'E' / UE

Substituting the given values, we get:

Scale factor = 10 cm / 2 cm

Simplifying the ratio, we get:

Scale factor = 5

Therefore, the scale factor is 5.

The correct answer is D. 5.0.