Use the figure to the right to find the value of PT. T is the midpoint of PQ. PT = 3x + 3 and TQ = 5x – 9

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Use the figure to the right to find the value of PT. T is the midpoint of PQ.
PT = 3x + 3 and TQ = 5x – 9

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  1. 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]

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