+128475 4x -3y + 12 = 0 rearrange as
3y = 4x + 12
y = (4/3)x + 4 (1)
A perpendicular through (10, 9) will have a negative reciprocal slope = -3/4
The equation of this line is
y= (-3/4) ( x -10) + 9
y = (-3/4)x + 30/4 + 9
y = (-3/4)x + 33/2 (2)
Find the x coordinate of the intersection of (1) and (2)
(4/3)x + 4 = (-3/4)x + 33/2
(4/3 + 3/4)x = 33/2 - 4
( 25/12)x = 25/2
x = ( 25/2) ( 12/25) = 12/2 = 6
And y = (4/3)(6) + 4 = 12
(6, 12)
This is the midpoint between (9,10) amd the reflection point
So we have
(10 + x)/2 = 6 (9 + y) / 2 = 12
10 + x = 12 9 + y = 24
x = 2 y = 15
The reflected point is (2,15)
Here's a graph : https://www.desmos.com/calculator/l4wolqqhos
