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
5x - 7
O 8 units
2x-2
X+1
B
A
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Et

Answer 1

Option (2)

Explanation:

Given question is incomplete; here is the complete question.

Point A is the midpoint of side XZ and point B is the midpoint of side YZ.

Triangle XYZ is cut by line segment AB. Point A is the midpoint of side XZ and point B is the midpoint of side YZ. The length of XY is (5x - 7), the length of AB is (x + 1), and the lengths of XA and ZA are (2x - 2). The lengths of YB and BZ are congruent.

What is AX ?

2 units

4 units

6 units

8 units

From the figure attached,

XYZ is a triangle having A and B as the midpoints of the sides XZ and YZ.

By the theorem of midpoints,

AB =
`(1)/(2)\text{(XY)}`

Since AB = (x + 1) and XY = (5x - 7)

(x + 1) =
`(1)/(2)(5x-7)`

2x + 2 = 5x - 7

5x - 2x = 2 + 7

3x = 9

x = 3

Therefore, side AB = 3 + 1 = 4 units

Side XY = (5x - 7)

= 15 - 7

= 8 units

Side XA = 2(x - 1)

= 4 units

Therefore, Option (2) will be the answer.