What is the slope of a line that is perpendicular to V(3, 2), W(8, 5)?

Question

Eva Adamson · Accepted Answer

See a solution process below:

The formula for find the slope of a line is: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))# Where #(color(blue)(x_1), color(blue)(y_1))# and #(color(red)(x_2), color(red)(y_2))# are two points on the line. Substituting the values from the points in the problem gives: #m = (color(red)(5) - color(blue)(2))/(color(red)(8) - color(blue)(3)) = 3/5# Let's call the slope of a perpendicular line: #color(blue)(m_p)# The slope of a line perpendicular to a line with slope #color(red)(m)# is the negative inverse, or: #color(blue)(m_p) = -1/color(red)(m)# Substituting the slope for the line in the problem gives: #color(blue)(m_p) = (-1)/color(red)(3/5) = -5/3#

Isaiah Anthony · Answer

undefined To find the slope of a line perpendicular to the line passing through points V(3, 2) and W(8, 5), first calculate the slope of the given line using the formula:

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

Substitute the coordinates of points V and W into the formula:

$$ \text{Slope} = \frac{5 - 2}{8 - 3} = \frac{3}{5} $$

The slope of the given line is $ \frac{3}{5} $.

To find the slope of a line perpendicular to this line, take the negative reciprocal of the slope of the given line:

$$ \text{Perpendicular Slope} = -\frac{1}{\text{Slope}} = -\frac{1}{\frac{3}{5}} = -\frac{5}{3} $$

Therefore, the slope of a line perpendicular to the line passing through points V(3, 2) and W(8, 5) is $ -\frac{5}{3} $.