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If P(2, m) is the midpoint of the line joining Q(m, n) and R(n, -4), find…

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If P(2, m) is the midpoint of the line joining Q(m, n) and R(n, -4), find the values of m and n

  • A. m = 2, n = 2
  • B. m = -2, n = 4
  • C. m = 0, n = 4
  • D. m = 4, n = 0

QUICK ANSWER…

C

DETAILS…  

Assuming two points on a straight line is given as (x y) (x y), then the mid-point between them will be:

If P(2, m) is the midpoint of the line joining Q(m, n) and R(n, -4), find the values of m and n.

Rearranging, we have:

n – 2m = 4 ……………………………..eq2

We now have two simultaneous equations.

n + m = 4

n – 2m = 4

Carrying out eq1 – eq2, we have:

(n – n) + (m – -2m ) = 4 – 4

0 + m + 2m = 0

3m = 0

m = 0

At this point, we don’t need to solve further for the value of n, this is because there is no other option that feature m = 0 apart from option C.

But for the sake of surety, lets solve further for the value of n.

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Substituting m = 0 into eq1, we have:

n – 2(0) = 4

n = 4

Option C has been verified.

Now for the right answer to the above question:

  1. Option A is incorrect.
  2. Option B is incorrect.
  3. C is correct.
  4. D is not the correct answer.

KEY-POINTS…

You may please note these/this:

  • Remember, the mid-point between two points is simply addition of both points divided by two.
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/ culled from 2019 JAMB-UTME mathematics question 22 /

If P(2, m) is the midpoint of the line joining Q(m, n) and R(n, -4), find... » QuizTablet
If P(2, m) is the midpoint of the line joining Q(m, n) and R(n, -4), find... » QuizTablet

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