Suppose XA = 3x and AY = 4x - 6. If A is the midpoint of XY, what is the length of XY?
3x 4x - 6
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X A Y
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X A Y
The trick in this problem is to see that if A is the midpoint, then XA = AY.
Since XA = AY, 3x = 4x - 6
Since XA = AY, 3x = 4x - 6
Subtract 3x from both sides.
3x - 3x = 4x - 3x - 6
0 = x - 6
Add 6 to both sides of the equation.
0 + 6 = x - 6 + 6
6 = x
3x - 3x = 4x - 3x - 6
0 = x - 6
Add 6 to both sides of the equation.
0 + 6 = x - 6 + 6
6 = x
To compute XA, you can either use 3x or 4x - 6
Using 3x, we get XA = AY = 3 × 6 = 16
Using 3x, we get XA = AY = 3 × 6 = 16
Using 4x - 6, we get XA = AY = 3 × 6 - 6 = 18 - 6 = 12
XY = XA + AY = 16 + 16 = 32
The length of XY is 32.
Assignment:
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