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2 years ago

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

Mathematics

1 answer:

Katyanochek1 [597]2 years ago

6 0

Answer:

Option (2)

Step-by-step 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 = $\frac{1}{2}\text{(XY)}$

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

(x + 1) = $\frac{1}{2}(5x-7)$

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.

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