Question

Write the the co-ordinate of midpoint of line segment joining the point A(x,y)and B(X2,y2)

Answer 1

Answer:

Step-by-step explanation:

Solution :-

What is mid Point? :-

Take a line-segment AB

Let, the co-ordinates of :-

$A = \sf(x_1,y_1)$

$B=\sf (x_2,y_2)$

If P is the mid-point of AB then m = n, the co-ordinates of AB are :-

$P=\sf \bigg(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\bigg)$

According to question :-

A = (x , y)

$B=\sf (x_2,y_2)$

Let , the midpoint be P :-

We know that :-

$P=\sf \bigg(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\bigg)$

$\implies x_1 = x , y_1 = y$

$x_2=x_2,y_2=y_2$

$P=\bigg(\dfrac{x+x_2}{2},\dfrac{y+y_2}{2}\bigg)$

$Since ,\: the\: co-ordinates\: of\: Mid-point\: are = \sf\bigg(\dfrac{x+x_2}{2},\dfrac{y+y_2}{2}\bigg)$

Know More :-

Formula of Internal division :-

$(x,y)=\bigg(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\bigg)$

Formula for external division :-

$(x,y)=\bigg(\dfrac{mx_2-nx_1}{m-n},\dfrac{my_2-ny_1}{m-n}\bigg)$