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

1 Answer
Jan 29, 2016

Answer:

slope = #11/7 #

Explanation:

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 #