How do you find the slope of a line perpendicular to V(3, 2), W(8, 5)?

2 Answers
May 20, 2017

Answer:

See a solution process below:

Explanation:

First, find the slope of the line V-W. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#

Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the 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#

Now, let's call the slope of the perpendicular line #m_p#

The slope of a perpendicular line is the negative inverse of the slope of the line it is perpendicular to, or:

#m_p = -1/m#

Substituting for #m# gives:

#m_p = -1/(3/5)#

#m_p = -5/3#

The slope of the line perpendicular to V-W is #-5/3#

May 20, 2017

Answer:

#m=-5/3#

Explanation:

#"to calculate the slope of the line VW use the "color(blue)"gradient formula"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))#
where m represents the slope and # (x_1,y_1),(x_2,y_2)" are 2 coordinate points"#

#"the points are " (x_1,y_1)=(3,2),(x_2,y_2)=(8,5)#

#rArrm_(color(red)(VW))=(5-2)/(8-3)=3/5#

#" the slope of a line perpendicular to VW is"#

#m_(color(red)"perpendicular")=-1/m_(color(red)(VW))#

#rArrm_(color(red)"perpendicular")=-1/(3/5)=-5/3#