Question

If the origin is the midpoint of the line segment joined by the points (2,3) (x,y) find x and y​

Answer 1

(- 2, - 3 )

Explanation:

Given the endpoints of a segment (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[0.5(x₁ + x₂), 0.5(y₁ + y₂ ) ]

Here (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (x, y) and the midpoint = (0, 0), thus

0.5(2 + x) = 0 , that is

2 + x = 0 ( subtract 2 from both sides )

x = - 2

0.5(3 + y) = 0, that is

3 + y = 0 ( subtract 3 from both sides )

y = - 3

Thus (x, y) = (- 2, - 3 )