Using the midpoint formula, the coordinates of the other endpoint, V is: B. (10, -25.8).
To find the coordinates of the midpoint of a segment, the midpoint formula is used, which is expressed as: M(x2 + x1/2, y2 + y1/2).
Given one endpoint of UV as, U(21.6, -8.2), and a midpoint of M(15.8, -17), let:
U(21.6, -8.2) = (x1, y1)
V(x, y) = (x2, y2)
Plug in the values into M(x2 + x1/2, y2 + y1/2):
M(15.8, -17) = (x2 + 21.6/2, y2 + (-8.2)/2)
Solve for x2
15.8 = (x2 + 21.6)/2
Multiply both sides by 2
2(15.8)= (x2 + 21.6)/2 × 2
31.6 = x2 + 21.6
Subtract both sides by 21.6
31.6 - 21.6 = x2 + 21.6 - 21.6
10 = x2
x2 = 10
Solve for y2:
-17 = (y2 + (-8.2))/2
Multiply both sides by 2
2(-17) = (y2 + (-8.2))/2 × 2
-34 = y2 + (-8.2)
-34 = y2 - 8.2
Add 8.2 to both sides
-34 + 8.2 = y2 - 8.2 + 8.2
-25.8 = y2
y2 = -25.8
The coordinates of the other endpoint, V is: B. (10, -25.8).
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