SOLUTION: what is the distance between y=1/2x,y=1/2x+5

Question 16749: what is the distance between
y=1/2x,y=1/2x+5
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
y=1/2x is the graph of a straight line with y intercept 0 and slope m=1/2
y=1/2x + 5 is the graph of a straight line with y intercept 5 and slope m = 1/2.

The second line is exactly the same as the first line, except that it is moved "up" 5 units.

If you rewrite these equations in standard form there is a formula for the distance from a point on a given line to another given line. Let's rewrite these equations in standard form as
y = 1/2x, which is 2y= x or x-2y=0
y=1/2x + 5, which is 2y = x + 10 or x-2y +10= 0

The formula (if I remember correctly from about 15 years ago!!)is :
Distance from a point to a given line: , where Ax+By+C = 0 is the equation of the line, and (x,y) is a given point (in this case, any point you choose to select from the other line--let's say the point (0,0) on the first line, since this is an easy point to see and to calculate).

So, let (0,0) be a point on the first line, and find the perpendicular distance from (0,0) to the line x-2y+10 = 0.

In the formula, A= 1, B=-2, C= 10, x=0, and y=0:

Someone may have an easier way, but this is what I recall from a LONG time ago!

R^2 at SCC
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