Question

The midpoint of Line

AB

is M(3, 3). If the coordinates of A are (2, -1), what are the coordinates of B?

Answer 1

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((x_(1)+x_(2))/(2), (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((2+x_(2))/(2), (-1+y_(2))/(2)\right)`

`\text { Now, by comparison, } (2+x_(2))/(2)=3 \text { and } (-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)

Answer 2

Answer: ( 4,7)

Explanation: