Question

Consider line segment DG, where D is (-4, 8) and G is (6, -2). Find the coordinates of point E such that DE:EG is 3:2.

Answer 1

Coordinates of E= (2,2)

Explanation:

Coordinates of D→ (-4,8) (x₁,y₁)

Coordinates of G→ (6,-2) (x₂,y₂)

Ratio= 3:2 (m:n)

Coordinates of E→ (
`(mx2+nx1)/(m+n)`,
`(my2+ny1)/(m+n)`)

= (
`(3x6+2x-4)/(3+2)`,
`(3x-2+2x8)/(3+2)`)

= (
`(18-8)/(5)`,
`(-6+16)/(5)`)

= (
`(10)/(5)`,
`(10)/(5)`)

= (2,2)

∴ coordinates of point E is (2,2).