Question

The midpoint of Line

Answer 1

Answer: ( 4,7)

Step-by-step explanation:

Answer 2

The midpoint of Line AB is M(3, 3). The co-ordinates of B are (4, 7)

Solution:

Given that, the midpoint of Line AB is M(3, 3)

And the coordinates of A are (2, -1)

We have to find what are the coordinates of B

$\text { The midpoint of a line } A\left(x_{1}, y_{1}\right) \text { and } B\left(x_{2}, y_{2}\right) \text { is given by } M=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{2}+y_{2}}{2}\right)$

$\text { Here } \mathrm{M}=(3,3) \text { and } \mathrm{A}\left(x_{1}, y_{1}\right)=(2,-1) \text { and } B\left(x_{2}, y_{2}\right)=?$

Substituting the values we get,

$(3,3)=\left(\frac{2+x_{2}}{2}, \frac{-1+y_{2}}{2}\right)$

$\text { Now, by comparison, } \frac{2+x_{2}}{2}=3 \text { and } \frac{-1+y_{2}}{2}=3$

$\begin{array}{l}{\rightarrow 2+x_{2}=6 \text { and }-1+y_{2}=6} \\\\ {\rightarrow x_{2}=6-2 \text { and } y_{2}=6+1} \\\\ {\rightarrow x_{2}=4 \text { and } y_{2}=7}\end{array}$

Hence, the co – ordinates of B is (4, 7)