Question

Use the diagram and the following information to find the value of x.

Note: T is the midpoint of .

PT = 6x + 4 and TQ = 52

ANSWER CHOICES x = 9.3 x = 10 x = 8 x =9

Answer 1

Given:

Given that PQ is a line segment.

T is the midpoint of PQ.

The length of PT is 6x + 4 and the length of TQ is 52.

We need to determine the value of x.

Value of x:

Since, we know that the midpoint of the line segment is a point that divides the segments into two congruent segments.

Thus, applying this property, we have;

PT = TQ

Substituting the values, we have;

`6x+4=52`

Subtracting both sides of the equation by 4, we get;

`6x=48`

Dividing by 6, we have;

`x=8`

Thus, the value of x is 8.

Hence, Option c is the correct answer.