Question

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?

Answer 1

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]