Question

The midpoint of ‾ AB is M(−3,−2). If the coordinates of A are ( 1 , − 7 ) , what are the coordinates of B?

Answer 1

B (- 7, 3 )

Explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is

M = (
`(x_(1)+x_(2) )/(2)` ,
`(y_(1)+y_(2) )/(2)` )

here (x₁, y₁ ) = A (1, - 7 ) and (x₂, y₂ ) = B (x, y )

apply the midpoint formula and equate to corresponding coordinates of M

`(1+x)/(2)` = - 3 ( multiply both sides by 2 )

1 + x = - 6 ( subtract 1 from both sides )

x = - 7

and

`(-7+y)/(2)` = - 2 ( multiply both sides by 2 )

- 7 + y = - 4 ( add 7 to both sides )

y = 3

coordinates of B = (- 7, 3 )