Find the midpoint on the line segment joining the points p1

Find the midpoint on the line segment joining the points p1 and p2. P1=(4-6); p2=(6,8)

Let C(x,y) is mid point on the line segment joining p1 and p2

equation of line segment

y -8 = [(-6-8)/(4-6)](x-6)

y-8 = 7(x-6)

7x-y = 34 -------(1)

as C(x,y) is mid point

so, [(x-4)^2 + (y+6)^2]^0.5 = [(x-6)^2+(y-8)^2]^0.5

By squaring both sides and solving

-8x +16 + 36 +12y = 36 -12x + 64-16y

4x+28y = 48

x + 7y =12 ------(2)

by solving equation 1 and 2

7x-y = 34 & x + 7y =12

multiplying equation 2 by 7

7x +49y = 84

subtracting equation 1

50y = 50 So, y =1

and x =5

So (5,1) is the mid point on the line segment