Question

In the diagram below of triangle T, U, VTUV, WW is the midpoint of start overline, T, V, end overline
TV
and XX is the midpoint of start overline, U, V, end overline
UV
. If W, X, equals, minus, 9, plus, 4, xWX=−9+4x, and T, U, equals, minus, 10, plus, 6, xTU=−10+6x, what is the measure of start overline, W, X, end overline
WX
?

Answer 1

Given that W is the midpoint of TV and X is the midpoint of UV, we can use the midpoint formula to find the coordinates of W and X.

Midpoint formula:
For midpoint M of points (x1, y1) and (x2, y2), the coordinates of M are ((x1 + x2)/2, (y1 + y2)/2).

Let's find the coordinates of W.
T = (-10, 6x)
V = (-9, 4x)

Coordinates of W: ((-10 + (-9))/2, (6x + 4x)/2)
= (-19/2, 5x)

Now let's find the coordinates of X.
U = (-9, 4x)
V = (-9, 4x)

Coordinates of X: ((-9 + (-9))/2, (4x + 4x)/2)
= (-9, 4x)

Now that we have the coordinates of W and X, we can find the distance between them using the distance formula.

Distance formula:
For two points (x1, y1) and (x2, y2), the distance between them is √((x2 - x1)^2 + (y2 - y1)^2).

Distance between W and X:
√((-9 - (-19/2))^2 + (4x - 5x)^2)
= √((1/2)^2 + (-x)^2)
= √(1/4 + x^2)
= √(x^2 + 1/4)

Therefore, the measure of WX is √(x^2 + 1/4).