Question

The endpoints of AB are A (-9, -1) and B (-3, 7). Find the coordinates of the midpoint M. *

Answer 1

Answer:

(-6 , 3)

Step-by-step explanation:

Co-ordinates of A = (-9,-1)

So let x¹ = -9 & y¹ = -1

Co-ordinates of B = (-3,7)

So let x² = -3 & y² = 7

According to Section formula ,

$(x',y') = ( \frac{mx^2 + nx^1}{m + n} ,\frac{my^2 +ny^1}{m + n} )$

where (x' , y') are the co-ordinates of the point which divides a line segment internally & (m , n) are the ratios in which the line is divided into.

As we have to find the co-ordinates of mid-point of AB , here m = n = 1 (∵ A mid-point always divides a line segment into 2 equal parts. Hence the ratio of length of both lines will be 1 : 1 )

Putting the values in the above formula gives :

$(x' , y') = (\frac{-3-9}{1+1} , \frac{7-1}{1+1} ) = (\frac{-12}{2} , \frac{6}{2} ) = (-6 , 3)$

∴ Co-ordinate of M = (-6 , 3)