# 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****₁**** y****₁****) (x****₂**** y****₂****), 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.**

**KEY-POINTS…**

**You may please note the****se/this****:**

**Remember, the mid-point between two points is simply addition of both points divided by two.****If you love our answers, you can login to comment and say hi to us at the comment section…**

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**/ culled from 2019 JAMB-UTME mathematics question 22 /**

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