Question

Use the figure to the right to find the value of PT. T is the midpoint of PQ.

Answer 1

Answer:

PT=30 units

Step-by-step explanation:

Given that:

Line PQ which has a mid point at T.

$PT = 3x + 9$ and

$TQ = 5x -5$

To find:

PT = ? in simplified terms.

Solution:

First of all, let us recall that mid point on a line segment is a point that divides the line in two equal parts.

In other words:

If a point B is the mid point of line segment AC, then AB = BC.

Here, the point T is the midpoint of PQ.

i.e. PT = TQ

$3x+9=5x-5\\\Rightarrow 3x-5x=-5-9\\\Rightarrow -2x=-14\\\Rightarrow x=7$

Putting value of $x$ in PT above:

$PT = 3x+9 = 3 \times 7 +9 \\\Rightarrow \bold{PT=30\ units}$