Question

f P(5, 4) is the midpoint of line segment DA and one endpoint has coordinates D(8, 2), what are the coordinates of A?

Answer 1

A (2, 6 )

Explanation:

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

[
`(1)/(2)` (x₁ + x₁ ),
`(1)/(2)` (y₁ + y₂ ) ]

here (x₁, y₁ ) = D(8, 2 )

let the coordinates of A be (x₂, y₂ )

then equate the x and y parts to the coordinates of the midpoint, that is

`(1)/(2)` (8 + x₂ ) = 5 ( multiply both sides by 2 to clear the fraction )

8 + x₂ = 10 ( subtract 8 from both sides )

x₂ = 2 ← x- coordinate of A

and

`(1)/(2)` (2 + y₂ ) = 4 ( multiply both sides by 2 to clear the fraction )

2 + y₂ = 8 ( subtract 2 from both sides )

y₂ = 6 ← y- coordinate of A

coordinates of A = (2, 6 )