Question

find the coordinates of the point which divides the line segment joining the points (4, -3) and (8.5) in the ratio 3:1 internally

Answer 1

The coordinates of the division point are (7, 3)

Explanation:

The coordinates of the point (x, y) which divides a segment with endpoints (x1, y1) and (x2, y2) at a ratio m1: m2 internally is (
`(m1x2+m2x1)/(m1+m2)` ,
`(m1y2+m2y1)/(m1+m2)` ).

∵ The line segment joining the points (4, -3) and (8, 5)

∴ x1 = 4 and x2 = 8

∴ y1 = -3 and y2 = 5

∵ The point divides the segment at ratio 3: 1

∴ m1 = 3 and m2 = 1

→ By using the rule above

∵ x =
`((3)(8)+(1)(4))/(3+1)` =
`(24+4)/(4)` =
`(28)/(4)`

∴ x = 7

∵ y =
`((3)(5)+(1)(-3))/(3+1)` =
`(15-3)/(4)` =
`(12)/(4)`

∴ y = 3

∴ The coordinates of the division point are (7, 3)