Question

Line segment has endpoints X(-10, -1) and Y(5, 15). To find the y-coordinate of the point that divides the directed line segment in a 5:3 ratio, the formula was used to find that . What is the y-coordinate of the point that divides into a 5:3 ratio? 1 2 9 10

Answer 1

9

Explanation:

CB = 16

CY: YB = 5 : 3

CY = 10 YB = 6

CY : YB = AX : XB = 5 : 3

∴ y coordinate of X is 9

Answer 2

9

Explanation:

Let's call P the point that divides the directed line segment in a 5:3 ratio

The x-coordinate of P is x1 + k*run

The y-coordinate of P is y1 + k*rise

where x1, y1 are the coordinates of X (the point on the left), these are x1 = -10 and y1 = -1.

k is computed as follows:

k = long part of XY/(long part of XY + short part of XY) = 5/(5+3) = 5/8

The run is the distance between X and Y on the x-axis,

run = 5 - (-10) = 15

The rise is the distance between X and Y on the y-axis,

run = 15 - (-1) = 16

Replacing into the previous equation:

The y-coordinate of the point that divides into a 5:3 ratio is = -1 + (5/8)*16 = 9