If T is the midpoint of PQ and PT = 3x+3, TQ = 7x-9, then PT = 12 units.
Determining the Value of PT
It is given that,
T is the midpoint of PQ ........ (1)
PT=3x+3 ......... (2)
TQ=7x-9 .......... (3)
From (1), the distance from P to T and the distance from T to Q will be equal.
⇒ PT = TQ [Since, a midpoint divides a line into two equal segments]
Hence, equating the equations of PT and TQ given in (2) and (3) respectively, equal, we get the following,
3x + 3 = 7x - 9
or 7x - 9 = 3x + 3
or 7x - 3x = 9 + 3
or 4x = 12
or x = 12/4
⇒ x = 3
Substitute this obtained value of x in equation (2)
PT = 3(3) + 3
PT = 9 + 3
PT = 12 units
Thus, if T is the midpoint of PQ, then the measure of PT and TQ is equal to 12 units.
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