Question

What is the midpoint of a line segment of A(6,8) and B(4,10)

Answer 1

Solution:-

Given

$\rm\implies A=(x_1=6,y_1=8)\:\: and \:\:B=(x_2=4 ,y_2=10)$

Formula:-

$\boxed{\rm x=\dfrac{x_1+x_2}{2} ,y=\dfrac{y_1+y_2}{2} }$

Now putting value on formula

$\rm x=\dfrac{6+4}{2} ,y=\dfrac{8+10}{2}$

$\rm x=\dfrac{10}{2} ,y=\dfrac{18}{2}$

$\rm x= 5\: and\: y = 9$

Hence

Required point is ( 5 , 9 )

More information

Proof of mid point formula

PROOF :-

let M be the mid point of the line segment joining the point A(x₁ , y₁ ) and B(x₂ , y₂ )

Then M divides AB in ratio 1:1

so by section formula the coordinates of M are

$\rm\bigg(\dfrac{1.x_2+1.x_1}{1+1} ,\dfrac{1.y_2+1.y_1}{1+1} \bigg)$

$\rm i.e,\bigg(\dfrac{x_1+x_2}{2} ,\dfrac{y_1+y_2}{2} \bigg)$

hence , the coordinate of the midpoint of AB are

$\rm \bigg(\dfrac{x_1+x_2}{2} ,\dfrac{y_1+y_2}{2} \bigg)$