Question

The point P is reflection of (-2,10) on the line 4x-3y=12. Find the coordinates of P.

Answer 1

DRAW IT FIRST !

equation of line is y = (4/3) x - 4
slope is 4/3
so slope of perpendicular is -3/4
what is line through( -2 , 10) with slope -3/4 ?
10 = -(3/4) (-2) + b
10 - 3/2 = b
b = 17/2 (not handy :( )
y = -(3/4) x + 17/2
our image is on that line but where?
The same distance the other side of the original line
where does the original line and the perp line intersect?
y = (4/3)x- 4
y = -(3/4)x + 17/2
------------------------ so
(4/3+3/4)x = 25/2
(16/12 + 9/12)x = 25/2
(25/12) x = 25/2
x = 6
y = 4
now it is easy
we went right 8 from - 2 to + 6
so go right 8 from x = 6
x = 14
we went down 6 from 10 to 4 so go down 6 again
y = -2

Answer 2

Awesome