Question

Julia was creating similar triangles in the coordinate plane. The first triangle had a rise of 3 and a run of 10. The second triangle had a rise of 7.5.

Analyze Julia’s work to see if she found the correct length of the run for the second triangle to be similar to the first triangle.


1. 
3
10
=
7.5
x

2. 75 = 3x

3. x = 25

Is Julia correct? If not, what was her mistake?
Yes, she is correct.
No, her proportion does not have the corresponding measures from corresponding figures in the same positions in the ratios.
No, she needed to have the product of the numerators equal to the product of the denominators.
No, she needed to multiply 7.5 to both sides.

Answer 1

Yes — Julia is correct.

Either by cross-multiplying:
3/10 = 7.5/x ⇒ 3x = 10·7.5 = 75 ⇒ x = 25.

Or by scale factor:
scale = 7.5/3 = 2.5, so run = 10·2.5 = 25.

The other choices describe mistakes that were not made (she did use corresponding measures and did cross-multiply correctly).