How do you find the slope of a line perpendicular to C(13, 2), D(15, -5)?

Question

Avery Alexander · Accepted Answer

the slope is #2/7# The slope of the line CD is #m=(-5-2)/(15-13)=-7/2# The slope of the line perpendicular to CD is: #m_1=-1/m=2/7#

Kennedy Adams · Answer

undefined To find the slope of a line perpendicular to the line passing through points C(13, 2) and D(15, -5), we first find the slope of the given line. Then, we take the negative reciprocal of that slope to find the slope of the perpendicular line.

The slope of the line passing through points C(13, 2) and D(15, -5) can be calculated using the formula:

$$ \text{Slope} = \frac{y_2 - y_1}{x_2 - x_1} $$

Substituting the coordinates of points C and D:

$$ \text{Slope} = \frac{-5 - 2}{15 - 13} = \frac{-7}{2} $$

To find the slope of the line perpendicular to this line, we take the negative reciprocal of $ \frac{-7}{2} $:

$$ \text{Perpendicular slope} = -\frac{1}{\frac{-7}{2}} = \frac{2}{7} $$

Therefore, the slope of the line perpendicular to the line passing through points C(13, 2) and D(15, -5) is $ \frac{2}{7} $.