Answer:
C(8, -16)
Explanation:
Line L has equation x + 2y = 16.
Solve for y.
2y = -x + 16
y = -(1/2)x - 8
Point B is on the x-axis, so its y-coordinate is 0.
x + 2y = 16
x + 0 = 16
x = 16
The coordinate of point B are (16, 0).
y = (-1/2)x + 8
The y-intercept of line AB is (0, 8).
E(0, 8)
AE = EB
From point B to point E, go 16 units left and 8 units up.
E(0, 8)
From point E to point A, also go 16 units left and 8 units up.
A(-16, 16)
Line M is perpendicular to line L, so the slope of line M is 2.
The equation of line M is
y = mx + b
m = 2
y = 2x + b
Line M includes point A(-16, 16)
16 = 2(-16) + b
b = 48
y = 2x + 48 (Equation of line M)
The x-intercept of line M is where y = 0.
0 = 2x + 48
2x = -48
x = -24
Point D has coordinates (-24, 0).
Since line DC is parallel to line L, to go from point D to point C is the same as going from point A to point B.
Go right 32 and down 16.
(-24, 0) becomes (8, -16)
C(8, -16)