SOLUTION: Find the distance between the point (-3,1) and the line y = -x+4. I know first I must find the equation of the perpendicular line, and I get y = -x-2. Then, I must find the poi

Question 1020098: Find the distance between the point (-3,1) and the line y = -x+4.
I know first I must find the equation of the perpendicular line, and I get y = -x-2. Then, I must find the point of intersection. In order to do this I know I must set both equations equal to one another as shown here: -x+4 = -x-2. This is where I get stuck. Could you please help me?
Found 2 solutions by Cromlix, solver91311:
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
If your line => y = -x + 4
Two lines that are perpendicular
to one another have gradients (slopes)
that multiply together to give -1
m1 x m2 = -1
If your original line has a gradient
of -1 the line perpendicular to it
would have a gradient of 1
-1 x m2 = -1
m2 = -1/-1
m2 = 1
Using the line equation
y - b = m(x - a)
with m = 1
(a,b) = (-3, 1)
y - 1 = 1(x - (-3))
y - 1 = x + 3
y = x + 3 + 1
y = x + 4
Using simultaneous equations:
y = -x + 4......(1)
y = x + 4.......(2)
Rearrange
y + x = 4........(1)
y - x = 4........(2)
Add (1) + (2)
2y = 8
y = 4
Substitute y = 4 into (1)
y + x = 4
4 + x = 4
x = 4 - 4
x = 0
Point of intersection - {0,4)
Distance between (0,4) and (-3,1)
√(x2 - x1)^2 + (y2 - y1)^2
√(-3 - 0)^2 + (1 - 4)^2
√(9) + (9)
√18
= 4.2 units
Hope this helps :-)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Perpendicular lines have NEGATIVE reciprocal slopes. So try deriving the equation of the perpendicular through the point (-3,1) again and see if you
don't have a better result.

As soon as you have the correct point of intersection, use the distance formula to calculate the distance between the given point and the point of
intersection.

where and are the coordinates of the given points.

John

My calculator said it, I believe it, that settles it

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