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Point M is the midpoint of segment QR. If QM = 2x + 5 and MR = 5x - 1, find the length of QR.
QR = 18, QR = 9, QR = -9, QR = 8
Solution:
Given, M is the midpoint of line segment QR.
⇒ QM = MR
⇒ 2x + 5 = 5x - 1
⇒ 5x - 2x = 5 + 1
⇒ 3x = 6
Divide both sides by 3,
⇒ x = 2
As we know that M divides the line segment QR in two equal parts
⇒ QM + MR = QR
Substitute the value of x = 2 in the equation QM = 2x + 5 and MR = 5x - 1
⇒ QR = 2(2) + 5 + 5(2) - 1
⇒ QR = 4 + 5 + 10 - 1
⇒ QR = 18 units.
Point M is the midpoint of segment QR. If QM = 2x + 5 and MR = 5x - 1, find the length of QR.
Summary:
The length of QR is 18 units, when M is the midpoint of line segment QR and QM = 2x + 5 and MR = 5x - 1.
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