Question

find the co-ordinate of the point which divides internally the line segment joining the points

(3,-2) & (-4,5 ) in the ratio 1:1
explanation​

Answer 1

(3,-2)= (x1=3 and y1=-2 )

(-4,5)=(x2=-4and y2=5)

by section formula ,

x=mx2+nx1/m+n

put the above given values:-

1×-4+1×3/1+1

=-4+3/2

=-1/2

y=my2+ny1/m+n

=1×5+1×-2/2

=5+(-2)/2

=5-2/2

=3/2

=(x=-1/2,y=3/2)

Answer 2

Let, the co-ordinate of point P be (X,Y)

Now, As we know that : when the ratio be

m:n

$X = \frac{ mx_{2} + n x_{1} }{m + n} \\ \\ = > X = \frac{1 \times ( - 4) +1 \times 3 }{1 + 1} \\ \\ = > X = \frac{ - 4 + 3}{2} = \frac{ - 1}{2} \\ \\ and \: \\ \\ Y = \frac{m y_{2} + n y_{1} }{m + n} \\ \\ = > Y = \frac{1 \times 5 + 1 \times ( - 2)}{1 + 1} \\ \\ = > Y = \frac{5 - 2}{2} \\ \\ = > Y = \frac{3}{2}$

Then, the co-ordinate of the point which divides internally ( -1/2,3/2)