Question

Find the coordinate of the point P that divides the directed line segment from A to B in the given ratio. Round the

coordinate to the nearest tenth if necessary.
A(7,-8),B(-7,-1);3 to 4

The coordinate of point P are

Answer 1

P(1, -5)

Explanation:

The segment must be divided into two parts in the ratio of 3:4.

That means the segment length to one part to the other part are in the ratio 7:3:4.

We find the distance in x and in y between the points, and we divide the horizontal and vertical distances in the same ratio.

Horizontal distance:

From x = 7 to x = -7, the distance is 14.

We need to divide a distance of 14 into two segments with the ratio of 3:4.

7x:3x:4x

14:3x:4x

14 = 3x + 4x

14 = 7x

The change in x = 2

7x:3x:4x

14:6:8

The distance in x from A is 6.

7 - 6 = 1

The x-coordinate is 1

Vertical distance:

From x = -8 to x = -1, the distance is 7.

We can easily conclude that to divide 7 into two parts with a ratio of 3:4, the parts will measure 3 and 4.

The change in y = 3

The distance in y from A is 3.

-8 + 3 = -5

The y-coordinate is -5

Answer: P(1, -5)