SOLUTION: The distance of the point (3,0) from the line {{{y=(1/2)x+1}}}

Question 13985: The distance of the point (3,0) from the line
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
the quoted line has gradient 1/2.

the line through (3,0) to this first line will have a gradient of -2 (look at my Lesson on straight lines, for the reason).

So, the second line equation is y=-2x+c... need to find c:

0 = -2(3) + c
0 = -6 + c
--> c = 6

--> equation is y=-2x+6

Right, we need to know the coordinates of th epoint where the 2 points cross...ie where the 2 lines are EQUAL...

so, we have y = (1/2)x + 1 = -2x + 6
(1/2)x = -2x + 5
x = -4x + 10
5x = 10
--> x = 2.

so from y = -2x + 6, we get
y = -2(2) + 6
y = -4 + 6
y = +2

so, point of intersection is (2,2).

So now you have 2 points (3,0) and (2,2)...find the length of that line...you do that :-)

jon.

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