Question

find coordinates of mid point of the line segments joining the point A(4,7) and B(0,1).​

Answer 1

Answer:

The midpoint of two endpoints of a line segment can be found by using the formula given below :

$\large \sf\bullet\:\:\:Midpoint =\Bigg\lgroup \dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2} \Bigg\rgroup$

Let point (4, 7) = $\sf (x_1,y_1)$ and point (0, 1) = $\sf (x_2,y_2)$

We simply just plug in our values into this formula to get our midpoint.

The mid point is :

$=>\sf \:\:\:Midpoint =\Bigg\lgroup \dfrac{4 + 0}{2} , \dfrac{7 + 1}{2} \Bigg\rgroup$

$=>\sf \:\:\:Midpoint =\Bigg\lgroup \dfrac{4 }{2} , \dfrac{8}{2} \Bigg\rgroup$

$=> \underline{ \boxed{\sf \:\:\:Midpoint =\bigg\lgroup 2 , 4 \bigg\rgroup}}$

We have the final answer as

$\bullet\:\:\large\sf \bigg\lgroup 2 , 4 \bigg\rgroup$

Answer 2

We're given,

$\sf{A(4, 7) = (x_1, y_1)}$

$\sf{P(\alpha, \beta) = ?}$

$\sf{B(0, 1) = (x_2, y_2)}$

P is the mid-point of AB

$\sf{\\}$

By Mid-point Formula, we know that, if $\sf P(\alpha, \beta)$ is the mid-point of AB, where $\sf A(x_1, y_1)$ and $\sf B(x_2, y_2)$, then :

$\quad\quad\bullet \sf \alpha = \dfrac{x_1 + x_2}{2}$

$\quad\quad\bullet \sf \beta = \dfrac{y_1 + y_2}{2}$

$\sf{\\}$

So, using Mid-point Formula,

$\sf{\alpha = \dfrac{x_1 + x_2}{2}}$

$\longrightarrow \sf{\alpha = \dfrac{4 + 0}{2}}$

$\longrightarrow \sf{\alpha = \dfrac{4}{2}}$

$\longrightarrow \sf{\alpha = 2}$

$\sf{\\}$

$\sf{\beta = \dfrac{y_1 + y_2}{2}}$

$\longrightarrow \sf{\beta = \dfrac{7 + 1}{2}}$

$\longrightarrow \sf{\beta = \dfrac{8}{2}}$

$\longrightarrow \sf{\beta = 4}$

$\sf{\\}$

Hence, the answer is,

$\longrightarrow \underline{\underline{\sf{\green{P(\alpha, \beta) = (2, 4)}}}}$