SOLUTION: On a graph 3x-5y=10 find the distance between the graphed slope and the point P(12,6) which is perpendicular to the slope when a line is drawn from point P to the slope. So in esse

Algebra ->  Trigonometry-basics -> SOLUTION: On a graph 3x-5y=10 find the distance between the graphed slope and the point P(12,6) which is perpendicular to the slope when a line is drawn from point P to the slope. So in esse      Log On


   

Question 1060097: On a graph 3x-5y=10 find the distance between the graphed slope and the point P(12,6) which is perpendicular to the slope when a line is drawn from point P to the slope. So in essence, I'm looking for the distance from P to the line of 3x-5y=10. Thank you very much
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The perpendicular distance between line 3x-5y=10 and point P (12,6)

Given line has slope 5%2F3.
Line perpendicular to given line and containing P is of equation y-6=%285%2F3%29%28x-12%29.

Where do these two lines meet?
Find intersection of:
-
3x-5y=10
-5y=10-3x
y=-10%2F5%2B3x%2F5
y=-2%2B3x%2F5
-
y-6=5x%2F3-%285%2F3%2912
y-6=5x%2F3-20
y=5x%2F3-14
-
Equating expressions for y,
-2%2B3x%2F5=5x%2F3-14
-2%2B14=5x%2F3-3x%2F5
12=5x%2F3-3x%2F5
12%2A15=25x-9x
12%2A15=16x
x=%2812%2A15%29%2F4
x=45
Use x to evaluate y,
y=5%2A45%2F3-14
y=5%2A15-14
y=61
-
Intersection Point, (45,61).


FIND DISTANCE BETWEEN (45, 61) and (12,6).
highlight_green%28sqrt%28%2845-12%29%5E2%2B%2861-6%29%5E2%29%29
highlight%28sqrt%284049%29%29


4049 is a prime number.