Question

If A(2,3), B(4,3), Find the x-co-ordinate of the mid point of seg AB.​

Answer 1

Answer:-

Given Points are A(2 , 3) ; B(4 , 3).

Let P be the midpoint of the line segment AB and it's coordinates be (x , y).

We know that,

$\sf \large{Mid \: point \: of \: a \: line \: segment \: = \: (\frac{x_{1} + x_{2} }{2} \: , \: \frac{y _{1} + y_{2} }{2})}$

Let ,

• x1 = 2
• x2 = 4
• y1 = 3
• y2 = 3.

Hence,

P(x , y) = [ (2 + 4)/2 , (3 + 3)/2 ]

→ P(x , y) = ( 6/2 , 6/2 )

→ P(x , y) = (3 , 3)

Hence,

• x = 3

• y = 3

Hence, the value of the x - coordinate of the midpoint of AB is 3.

Some Important Formulae:

• Distance between two points with coordinates (x1 , y1) ; (x2 , y2) is $\sf\large{ \sqrt{{(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2}}}$

• section formulae:

The point P divides the points (x1 , y1) and (x2 , y2) in the ratio m : n .

$\sf\large{1. internally \:is\: (\frac{mx_2 + nx_1}{m + n} \: , \: \frac{my_2 + ny_1}{m + n});m + n ≠ 0}$

$\sf\large{2. externally\: is \: \frac{mx_2 - nx_1}{m - n} \: , \: \frac{my_2 - ny_1}{m - n} ); m ≠ n}$