Question

The midpoint pf ab is m ( 0,-1) . If the coordinates of a are (4,3), what are the coordinates of b

Answer 1

The coordinate of point B is (-4, -5).

Explanation:

Given:

M is the midpoint of a AB

let
`A = (4,3) = (x1,y1)\ say\\ B = (x2,y2)\ say\\M = (0,-1)= (x,y)\ say`

To Find:

`B = (x2,y2) = ?`

Solution:

As M is the midpoint of
`\vec{AB}` so applying midpoint formula we have

X coordinate i.e x and Y coordinate i.e y given by

`x = (x1 + x2)/(2)\\ and\\y = (y1 + y2)/(2)`

On substituting the values for X1, X2, X and Y we will get

`0 =(4 + x2)/(2)\\0 = 4 + x2\\x2 = -4\\and\\-1 = (3 + y2)/(2) \\-2 = 3 + y2\\y2 = -2 - 3\\y2 = -5`

So the coordinates for B (x2,y2) is B (-4,-5).