Question

C is midpoint of PQ. P is (4,m) C is (n, -1) and Q is (-2,4) find m and n

Answer 1

Answer:m= -6 & n=1

Step-by-step explanation:

Given that ,

P is (4,m)

Q is (-2,4)

And C(n,-1) is the midpoint of PQ

THEREFORE,

{4+(-2)}/2=n

Or,2/2=n

Therefore n=1

Also, (m+4)/2=-1

Or, m+4=-2

Or, m=-2-4

Therefore m= -6

Answer 2

The value of m=-6 and n=1.

Explanation:

We know that if M is a midpoint of line segment joining A(a,b) and B(c,d), then coordinates of M is given by :-

$(x,y)=(\dfrac{a+c}{2}, \dfrac{b+d}{2})$

Given : Coordinates of C is (n, -1)

Coordinates of P is (4,m) and Coordinates of Q is (-2,4) .

Since C is midpoint of PQ.

Then, $(n,-1)=(\dfrac{4+(-2)}{2},\ \dfrac{m+4}{2})$

$(n,-1)=(\dfrac{4-2}{2},\ \dfrac{m+4}{2})$

Compare x and y coordinate individually ,

$n=\dfrac{2}{2}=1\\\\\Rightarrow\ n=1$

$\dfrac{m+4}{2}=-1\\\\\Rightarrow\ m+4=-2\\\\\Rightarrow\ m=-2-4=-6$

Hence, the value of m=-6 and n=1.

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