Question

The midpoint of an is me -2,-6 if the coordinates of a are 1,-4 what are the coordinates of b

Answer 1

Given:

`\text{ The midpoint of }\bar{AB}\text{ is }M(-2,-6).\text{ Co-ordinates of A are }(1,-4).`

Required:

What are the coordinates of B?

Step-by-step explanation:

We know the mid-point of of line between two points is:

`(x,y)=((x_1+x_2)/(2),(y_1+y_2)/(2))`

Now, let point B(x1, y1)

`\begin{gathered} (-2,-6)=((1+x_1)/(2),(-4+y_1)/(2)) \\ \text{ Equate Co-ordinates} \\ (1+x_1)/(2)=-2 \\ 1+x_1=-4 \\ x_1=-5 \\ and \\ (-4+y_1)/(2)=-6 \\ -4+y_1=-12 \\ y_1=-8 \end{gathered}`
`\text{ Point B is }(-5,-8)`

Answer:

Hence, (-5,-8) is point B.