Question

The vertical line is a perpendicular bisector for AB. If the distance from A to the bisector is 8 cm and the total length of AB (5x-4), what is the value of x?

a) 4
b) 5
c) 6
d) 7

Answer 1

The value of x is found by setting the half-length of AB, which is (5x - 4)/2, equal to the distance from A to the perpendicular bisector, which is 8 cm. Solving this equation, we find that x = 4.

Step-by-step explanation:

To find the value of x for the given problem, we should recognize that the perpendicular bisector of line segment AB divides it into two equal parts. Therefore, the distance from A to the bisector (8 cm) is half of the entire length of AB. Since the total length of AB is given by the expression 5x - 4, each half of AB is (5x - 4)/2.

Setting the half-length equal to the known distance from A to the bisector, we have:

• (5x - 4)/2 = 8

Multiplying both sides by 2 to eliminate the fraction, we get:

• 5x - 4 = 16

Adding 4 to both sides:

• 5x = 20

Dividing by 5 to solve for x:

• x = 4

So, the value of x is 4, which corresponds to option a.