Question

In the diagram below B is the midpoint of AC if AB equals 2X and BC equals X squared -24 find the value of X and the length of AC

Answer 1

If B is the midpoint

• AB=BC
• x²-24=2x
• x²-2x-24=0
• x²-6x+4x-24=0
• (x-6)(x+4)=0
• x=6,-4

Distance is positive

• x=6

AC

• 2(2x)
• 4x
• 4(6)
• 24

Answer 2

x = 6

AC = 24

Explanation:

The midpoint divides the segment into two congruent parts.

AB = BC

BC -AB = 0

x^2 -24 -2x = 0

(x -1)^2 = 25 . . . . . . add 25, write as a square

x = 1 +√25 = 6 . . . . only the positive solution is of interest.

AC = 2(AB) = 2(2x) = 4(6) = 24

The value of X is 6, and the length of AC is 24 units.