Question

point a is the midpoint of side xz and point b is the midpoint of side yz. what is ax? 2 units 4 units 6 units 8 units

Explanation:

Step1: Use the mid - segment theorem

The mid - segment theorem states that the length of the mid - segment (a segment connecting the midpoints of two sides of a triangle) is half the length of the third side. So, \(5x - 7 = 2(x + 1)\).

Step2: Solve the equation for \(x\)

Expand the right - hand side: \(5x-7 = 2x + 2\).
Subtract \(2x\) from both sides: \(5x-2x-7=2x - 2x+ 2\), which gives \(3x-7 = 2\).
Add \(7\) to both sides: \(3x-7 + 7=2 + 7\), so \(3x=9\).
Divide both sides by \(3\): \(x=\frac{9}{3}=3\).

Step3: Find the length of \(AX\)

Since \(AX = 2x - 2\), substitute \(x = 3\) into the expression. Then \(AX=2\times3 - 2\).
Calculate \(2\times3-2=6 - 2 = 4\).

Answer:

4 units