Question

V is the midpoint of UW. If UV= x+8 and V W = 9x, what is UV?

8
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5

Answer 1

To find the length of UV, we can use the midpoint formula.

Step-by-step explanation:

To find the length of UV, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (V) are the average of the coordinates of the endpoints (U and W). In this case, since V is the midpoint of UW, we can write the equation:

V = (1/2)(U + W)

Substituting the given values, we have:

x+8 = (1/2)(x+9x)

Simplifying the equation, we get:

x+8 = (1/2)(10x)

Multiplying both sides of the equation by 2, we get:

2(x+8) = 10x

Expanding the equation, we get:

2x + 16 = 10x

Subtracting 2x from both sides of the equation, we get:

16 = 8x

Dividing both sides of the equation by 8, we get:

x = 2

Therefore, the length of UV is x + 8 = 2 + 8 = 10 units.