Raymond B. answered • 01/18/23
Math, microeconomics or criminal justice
the reflected point is (14,-2)
it definitely helps to plot the points and graph the lines
4x -3y = 12
reflect the point (-2, 10) over the above line
which is the same line as
3y=4x-12
y=4x/3 -4 which has slope = 4/3
a perpendicular line has a negative inverse slope -3/4
y=-3x/4 + b
10=-3(-2)/4 +b
10=3/2 +b
b = 10-3/2 = 17/2
y = -3x/4 +17/2 is the perpendicular line
find the distance from (-2,10) to the intersection of the perpendicular lines
the intersection is when 4x/3-4 = -3x/4+17/2
4x/3 +3x/4 = 17/2+4
16x/12 +9x/12 = 25/2
25x/12 =25/2
x/6 =1
x = 6,
y =-3(6)/4 +17/2 =-3(3)/2+17/2 =8/2= 4
intersection point is (6, 4)
from there to (-2, 10)
= d= 10 where
d^2 = 8^2 + (6)^2 = 64+36 =100
d = sqr100 = 10
the reflected point is 10 on the other side of the line
6 is 8 greater than -2
10 is 6 greater than 4
reflected point is
8 +6 = 14 = x coordinate of the reflected point
6 less than 4 = -2 = y coordinate of the reflected point
(14,-2) is the reflection across the given line
from (14, -2) to (6, 4) the distance
= d=10
where d^2 = 8^2 + (6)^2 = 64 + 36 = 100
d=sqr100= 10
(14,-2) is the same distance on one side of the given line as (-2,10) is on the other side of the given line
with their midpoint (6,4) on the line 4x-3y=12
4(6)-3(4)=12
24-12=12
