If P(2, m) is the midpoint of the line joining Q(m, n) and R(n, -4), find…
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
Assuming two points on a straight line is given as (x₁ y₁) (x₂ y₂), then the mid-point between them will be:
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.
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:
- Option A is incorrect.
- Option B is incorrect.
- C is correct.
- D is not the correct answer.
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
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