Question

The midpoint of AB is M(7, 5). The coordinates of point A are (4, 1). Find the coordinates of point B. Explain

Answer 1

B (10, 9 )

Explanation:

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

M (
`(x_(1)+x_(2) )/(2)` ,
`(y_(1)+y_(2) )/(2)` ) ← midpoint formula

use the formula to find the x and y coordinate by equating to the corresponding coordinates of M.

let (x₁, y₁ ) = A (4, 1 ) and (x₂, y₂ ) = B (x, y ) ← to be found

`(4+x)/(2)` = 7 ( multiply both sides by 2 to clear the fraction )

4 + x = 2 × 7 = 14 ( subtract 4 from both sides )

x = 10

and

`(1+y)/(2)` = 5 ( multiply both sides by 2 to clear the fraction )

1 + y = 2 × 5 = 10 ( subtract 1 from both sides )

y = 9

coordinates of B = (10, 9 )