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):
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