Question

In triangle ABC the lines m, n, and p are perpendicular bisectors of the side and intersects at point T. AT = 2x-5, CT= 3(x-1) and BT = 5y+1 A. What's is the value of x

Answer 1

x = -2

Explanation:

Any point on a perpendicular bisector is equidistant from the endpoints of the segment it bisects. Hence, we have ...

AT = CT

2x -5 = 3(x -1) . . . . . substitute the given expressions

2x -5 = 3x -3 . . . . . . eliminate parentheses

2x -2 = 3x . . . . . . . . add 3

-2 = x . . . . . . . . . . . . subtract 2x

The value of x is -2.

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Comment on the problem

The value of x shown is the algebraic solution to the problem. This value of x makes AT = CT = -9. A line segment cannot have negative length, so we consider this geometry problem to have "no solution." That is, perhaps, unfortunate--another case of poor math curriculum editing.