Question

Wz is perpendicular to vy, wz bisects vy , vz = 2x + 4, and ZY = 3x – 4. What is ZY?

Answer 1

Wz is perpendicular to vy, wz bisects vy , vz = 2x + 4, and ZY = 3x – 4. What is ZY?

2x+4 = 3x-4

-4 -4

(subtract 4 from both sides)

2x= 3x - 8

-3x -3x

(subtract 3x from both sides)

-1x= -8

(divide by -1 on both sides)

x=8

(or ZY= 8 actually)

Answer 2

Hence, the value of:

zy=20

Explanation:

It is given that:

wz is perpendicular to vy.

Also wz bisects vy.

We are asked to find the length of the segment zy?

Such that we are given:

vz=2x+4 , zy=3x-4

Since wz bisects vy that means it divides line segment vy into two equal lengths. i.e. vz=zy

Also,

vz=2x+4 and zy=3x-4

Hence,

2x+4=3x-4

⇒ 3x-2x=4+4 ( since taking variable term to one side of the equation and constant term to the other)

⇒ x=8

Hence, the length of segment zy is:

3x-4=3×8-4

3x-4=24-4=20

Hence, the length of zy is 20