Question

Please help me thank you

Answer 1

!.  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 ....