What is the equation of the line that is perpendicular to the line passing through #(5,3)# and #(8,8)# at midpoint of the two points?

1 Answer
Dec 28, 2015

Answer:

The equation of the line is # 5*y+3*x=47#

Explanation:

The co-ordinates of the mid -point is #[(8+5)/2 , (8+3)/2]# or #(13/2,11/2)# ; The slope m1 of the line passing through #(5,3) and (8,8)# is # (8-3)/(8-5)# or#5/3#; We know the cond ition of perpendicularity of two lines is as # m1*m2 = -1# where m1 and m2 are the slopes of the perpendicular lines. So the slope of the line will be # (-1/(5/3))# or #-3/5# Now the equation of line passing through the mid point is #(13/2,11/2)# is #y-11/2 = -3/5(x-13/2)# or #y=-3/5*x+39/10+11/2# or #y + 3/5*x = 47/5# or #5*y+3*x=47#[Answer]