Answer:
PT=30 units
Step-by-step explanation:
Given that:
Line PQ which has a mid point at T.
[tex]PT = 3x + 9[/tex] and
[tex]TQ = 5x -5[/tex]
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
[tex]3x+9=5x-5\\\Rightarrow 3x-5x=-5-9\\\Rightarrow -2x=-14\\\Rightarrow x=7[/tex]
Putting value of [tex]x[/tex] in PT above:
[tex]PT = 3x+9 = 3 \times 7 +9 \\\Rightarrow \bold{PT=30\ units}[/tex]
