Question

Right triangle ABC is shown below.

On a coordinate plane, a line goes through (0, negative 2) and (3, 1). Triangle A B C has a rise of 4 and run of 3.

A similar right triangle would be created by a rise of 8 and a run of
.

Answer 1

To find the missing value for the run of a similar right triangle that has a rise of 8, we can use the concept of similar triangles.

Given that triangle ABC has a rise of 4 and a run of 3, the ratio of rise to run is:

\[
\text{Ratio} = \frac{\text{rise}}{\text{run}} = \frac{4}{3}
\]

For a similar triangle with a rise of 8, we can set up a proportion to find the corresponding run (let's call it \( x \)):

\[
\frac{8}{x} = \frac{4}{3}
\]

Now we can cross-multiply to solve for \( x \):

\[
4x = 8 \cdot 3
\]
\[
4x = 24
\]
\[
x = \frac{24}{4} = 6
\]

Thus, the run corresponding to a rise of 8 in a similar right triangle is 6.