Question
Right triangle ABC is shown below.
On a coordinate plane, a line goes through (negative 1, 0) and (0, 3). A triangle has a rise of 3 and run of 1.
A similar right triangle would be created by a run of 4 and a rise of
On a coordinate plane, a line goes through (negative 1, 0) and (0, 3). A triangle has a rise of 3 and run of 1.
A similar right triangle would be created by a run of 4 and a rise of
Answers
GPT-4o mini
To find the rise of the similar right triangle with a run of 4, we first need to determine the slope of the original triangle.
Given that the original triangle has a rise of 3 and a run of 1, the slope (m) can be calculated as follows:
\[
m = \frac{\text{rise}}{\text{run}} = \frac{3}{1} = 3.
\]
For similar triangles, the ratio of the rise to the run must remain consistent. Therefore, if the new triangle has a run of 4, we can use the slope to find the corresponding rise.
Using the slope of 3:
\[
\text{slope} = \frac{\text{rise}}{\text{run}} \implies 3 = \frac{\text{rise}}{4}.
\]
Now we can solve for the rise:
\[
\text{rise} = 3 \cdot 4 = 12.
\]
Hence, for the similar right triangle with a run of 4, the rise is **12**.
Given that the original triangle has a rise of 3 and a run of 1, the slope (m) can be calculated as follows:
\[
m = \frac{\text{rise}}{\text{run}} = \frac{3}{1} = 3.
\]
For similar triangles, the ratio of the rise to the run must remain consistent. Therefore, if the new triangle has a run of 4, we can use the slope to find the corresponding rise.
Using the slope of 3:
\[
\text{slope} = \frac{\text{rise}}{\text{run}} \implies 3 = \frac{\text{rise}}{4}.
\]
Now we can solve for the rise:
\[
\text{rise} = 3 \cdot 4 = 12.
\]
Hence, for the similar right triangle with a run of 4, the rise is **12**.