Question

Point A is the midpoint of side XZ and point B is the midpoint of side YZ. Triangle X Y Z is cut by line segment A B. Point A is the midpoint of side X Z and point B is the midpoint of side Y Z. The length of X Y is 5 x minus 7, the length of A B is x + 1, and the lengths of X A and Z A are 2 x minus 2. The lengths of Y B and B Z are congruent. What is AX? 2 units 4 units 6 units 8 units

Answer 1

Answer:

B. 4units

Step-by-step explanation:

Find the diagram attached. The diagram is a similar triangle.

From the diagram, XZ/XY = CA/AB

Given XZ = 2x-2+2x-2 = 4x-4

XY =5x-7

CA = 2x-2

AB= x+1

On substituting this parameters into the formula to get x first

4x-4/5x-7 = 2x-2/x+1

cross multiply

(4x-4)(x+1) = 5x-7(2x-2)

open the parenthesis

4x²+4x-4x-4 = 10x²-10x-14x+14

4x²-4 = 10x²-24x+14

10x²-4x²-24x+14+4 = 0

6x²-24x+18 = 0

x²-4x+3 = 0

x²-3x-x+3 = 0

x(x-3)-1(x-3)  =0

(x-3)(x-1) = 0

x = 3 and 1

Next is to get length AX.

Given AX = 2x-2

Substitute x = 3 into the expression

AX = 2(3)-2

AX = 6-2

AX = 4 units

Hence the measure of length AX is 4 units