Question

OQ=4x+2,OQ=4x+2, PQ=4x-10,PQ=4x−10, and OP=3x-3,OP=3x−3, determine the numerical length of OQ

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Answer 1

22

Explanation:

The segment addition theorem tells us the whole is the sum of the parts. We can use this to write an equation relating the expressions for segment length.

Setup

OQ = OP +PQ . . . . . segment addition theorem

4x +2 = (3x -3) +(4x -10) . . . . substitute given expressions

Solution

15 = 3x . . . . . . add 13 -4x to both sides

5 = x . . . . . . . divide by 3

OQ = 4x +2 = 4(5) +2 = 22

The length of OQ is 22 units.