Answer:
[tex]PQ = 42[/tex]
Step-by-step explanation:
Given
[tex]PT = 3x + 3[/tex]
[tex]TQ = 5x - 9[/tex]
Midpoint, T
Required
Determine PT
First, the value of x has to be calculated;
Since T is the midpoint, then:
[tex]PT = TQ[/tex]
This implies
[tex]3x + 3 = 5x - 9[/tex]
Solve for x
[tex]3x - 5x = -3 - 9[/tex]
[tex]-2x = -12[/tex]
[tex]x = -12/-2[/tex]
[tex]x = 6[/tex]
Length PQ can then be calculated using:
[tex]PQ = PT + TQ[/tex]
[tex]PQ = 3x +3 + 5x -9[/tex]
Collect Like Terms
[tex]PQ = 3x+ 5x +3 -9[/tex]
[tex]PQ = 8x -6[/tex]
Substitute 6 for x
[tex]PQ = 8 * 6 - 6[/tex]
[tex]PQ = 48 - 6[/tex]
[tex]PQ = 42[/tex]
