Answer:
1. 32 units
2. C(-15, -4) and D(17, -4)
Step-by-step explanation:
1.
The midpoint divides CD into two segments that are the same length:
CM = MD
8(x -2) = 4(5x -16)
8x -16 = 20x -64 . . . eliminate parentheses
48 = 12x . . . . . . . . . add 64 -8x
x = 4 . . . . . . . . . . . divide by 12
Then the length of CD is ...
CD = 2·CM = 2(8(x -2)) = 2(8(4-2))
CD = 32
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2.
If we put C and D on the same horizontal line as M, their coordinates are ...
C = M -(16, 0) = (1,-4) -(16, 0) = (-15, -4)
D = M +(16, 0) = (1, -4) +(16, 0) = (17, -4)
Coordinates C and D that have M(1, -4) as a midpoint are ...
C(-15, -4) and D(17, -4).
