Question

What are the coordinates of the point in the directed line segment from (-2,-8) to (5,-1) that partitions the segment into the ratio of 1 to 6?

Answer 1

The coordinates of the point P in the directed line segment from (-2,-8) to (5,-1) that partitions the segment into the ratio of 1 to 6 will be:

• (x, y) = (-1, -7)

Explanation:

Let P be the point.

As the point P is in the directed line segment from (-2,-8) to (5,-1) into the ratio of 1 to 6

i.e.

(x₁, y₁) = (-2,-8)

(x₂, y₂) = (5,-1)

Rise = y₂ - y₁ = -1 - (-8) = -1 + 8 = 7

Run = x₂ - x₁ = 5 - (-2) = 5 + 2 = 7

1 : 6 ratio means the point P lies at

`(1)/(6+1)=(1)/(7)=14\%`

Thus,

rise for P = 7 × 14% = 1

run for P = 7 × 14% = 1

Thus, coordinates of P will be:

x = -2 + 1 = -1

y = -8 + 1 = -7

Thus,

The coordinates of the point P in the directed line segment from (-2,-8) to (5,-1) that partitions the segment into the ratio of 1 to 6 will be:

• (x, y) = (-1, -7)