Question

B is the midpoint of AC. AB =2x-1 and AC= 3x+2.

X=
AB=
BC=
AC=

Answer 1

• x = 4
• AB = 7
• BC = 7
• AC = 14

Explanation:

You want the values of x, AB, BC, and AC if B is the midpoint of AC, and AB = 2x-1 and AC = 3x+2.

Midpoint

The midpoint of a line segment divides the segment into two congruent parts. Each part is half the length of the whole segment.

AB +BC = AC

Solution

AB +AB = AC . . . . . . AB ≅ BC

(2x -1) +(2x -1) = (3x +2)

x = 4 . . . . . . . . . . . add 4-3x and simplify

AB = 2x -1 = 2(4) -1 = 7

BC = AB = 7

AC = 3x +2 = 3(4) +2 = 14

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