Question

Find the mid-point of the line segment joining the points (1, 3) and (3, 1).
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Answer 1

Given :

• A(1, 3)
• B(3, 1)

To Find :

The Mid - Point.

Solution :

Analysis :

Here we have to use the mid point formula. Then by substituting the values we can find the mid point.

Required Formula :

$\boxed{\bf(x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}$

where,

• (x₁, y₁) = points of first coordinates
• (x₂, y₂) = points of second coordinates

Explanation :

• A(1, 3)
• B(3, 1)

We know that if we are given the coordinates of two points and is asked to find the mid point then our required formula is,

$\\ :\implies\sf(x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

where,

• x₁ = 1
• x₂ = 3
• y₁ = 3
• y₂ = 1

Using the required formula and substituting the required values,

$\\ :\implies\sf(x,y)=\left(\dfrac{1+3}{2},\dfrac{3+1}{2}\right)$

$\\ :\implies\sf(x,y)=\left(\dfrac{4}{2},\dfrac{4}{2}\right)$

$\\ :\implies\sf(x,y)=\left(\dfrac{\not{4}\ \ ^2}{\not{2}},\dfrac{\not{4}\ \ ^2}{\not{2}}\right)$

$\\ :\implies\sf(x,y)=\left(2,2\right)$

$\\ \therefore\boxed{\bf(x,y)=\left(2,2\right)}$

The mid point of the line is (2, 2).

Explore More :

Section Formula :

$\sf(x,y)=\left(\dfrac{m_1x_2+m_2x_1}{m_1+m_2},\dfrac{m_1y_2+m_2y_1}{m_1+m_2}\right)$