Home > Algebra > Equations of Perpendicular Lines

What is the slope of any line perpendicular to the line passing through #(4,5)# and #(-7,12)#?

Answer 1

Nathan Axel

slope = #11/7 #

the slope of a line joining 2 points can be calculated using the

#color(blue)( " gradient formula ")#

# m = (y_2 - y_1)/(x_2 - x_1 ) #

where # (x_1 , y_1 ) color(black)( and") (x_2 , y_2 )#

are 2 points.

let # (x_1 , y_1 )= (4 , 5 ) color(black)(" and ") (x_2 , y_2 ) = (-7 , 12)#

hence # m = (12 - 5 )/(- 7 - 4 ) = 7/(-11) = -7/11 #

The 'product' of the gradients of perpendicular lines is

# m_1 . m_2 = - 1 #

If # m_2# represents the gradient of the perpendicular line .

then # -7/11 xxm_2 = -1 color(black)( " and ") m_2 = -1/(-7/11) = 11/7 #

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Hazel Anglin

To find the slope of the line passing through two points (x1, y1) and (x2, y2), you use the formula: slope = (y2 - y1) / (x2 - x1). Given the points (4, 5) and (-7, 12), the slope of the line passing through them is (12 - 5) / (-7 - 4) = 7 / -11. The slope of any line perpendicular to this line is the negative reciprocal of this slope. Therefore, the slope of any line perpendicular to the given line is 11/7.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.