!. Find the equation of line l
(-4, 2) , (3, -5)
m = (-5-2)/(3+4) = -7/7 = -1
y = mx + b
y = -x +b ( take a point and substitute x,y )
2 = 4 + b, b = -2
y = -x -2
Slope of perpendicular line m =1 ( negative reciprocal)
y = x + b
2 = 1 + b, b =1
y = x +1
Now you need the point of intersection ( where they are equal to each other)
- x -2 = x+1
-3 = 2x, x = - 3/2
Plug x =-3/2 in either line to find y
y = -3/2 +2/2 = - 1/2
We have the point where the perpendicular meets the other line:
M( -3/2, -1/2)
We now have two points: P (1,2) and M and we can use the distance formula:
D =sqrt ( x2-x1)^2 + (y2-y1)^2
D = sqrt ( 1+3/2)^2 + (2+1/2) ^2 =sqrt ((5/2)^2 + (5/2)^2 =sqrt ( 50/4) = 5/2sqrt2
wow this one was long ....
