Math / Geometry

QuestionPart 1 of 3 (a) Find the run, rise, and slope given by triangle $A B C$ . run: $\square$ rise: $\square$ slope: $\square$

Studdy Solution

STEP 1

1. We have a right triangle $ABC$ on a coordinate plane.
2. The coordinates of point $A$ are $(12, 2)$ .
3. The coordinates of point $B$ are $(-2, 0)$ .
4. The coordinates of point $C$ are $(12, 0)$ .
5. The line segment $AB$ is the hypotenuse.
6. The horizontal leg is $BC$ and the vertical leg is $AC$ .

STEP 2

1. Calculate the run (horizontal distance) between points $B$ and $C$ .
2. Calculate the rise (vertical distance) between points $A$ and $C$ .
3. Calculate the slope of line segment $AB$ .

STEP 3

Calculate the run, which is the horizontal distance between points $B$ and $C$ . Since both points have the same y-coordinate ( $y = 0$ ), the run is the difference in their x-coordinates:
$\text{Run} = |x_C - x_B| = |12 - (-2)| = |12 + 2| = 14$

STEP 4

Calculate the rise, which is the vertical distance between points $A$ and $C$ . Since both points have the same x-coordinate ( $x = 12$ ), the rise is the difference in their y-coordinates:
$\text{Rise} = |y_A - y_C| = |2 - 0| = 2$

STEP 5

Calculate the slope of line segment $AB$ . The slope is given by the formula:
$\text{Slope} = \frac{\text{rise}}{\text{run}} = \frac{y_B - y_A}{x_B - x_A}$
Substitute the coordinates of points $A$ and $B$ :
$\text{Slope} = \frac{0 - 2}{-2 - 12} = \frac{-2}{-14} = \frac{1}{7}$
The run, rise, and slope of triangle $ABC$ are:
Run: $14$ , Rise: $2$ , Slope: $\frac{1}{7}$

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