Question

the question is asking, "find the coordinates of the point k, two thirds of the distance from L(-5,-1) to R(1,2)

Answer 1

The coordinates of point K that is two-thirds of the distance from L(-5, -1) to R(1, 2) are calculated using the section formula, resulting in K being located at (-1, 1).

Step-by-step explanation:

To find the coordinates of the point K that is two-thirds of the distance from L(-5, -1) to R(1, 2), we use the concept of section formula in coordinate geometry. The section formula provides a way to calculate the coordinates of a point that divides the line segment connecting two points in a specific ratio.

Let's denote the coordinates of point L as (x1, y1) and the coordinates of point R as (x2, y2). The coordinates of point K, which divides the line segment LR in the ratio of 2:1, can be determined by the following formulas:

1. Kx = (2*x2 + x1) / 3
2. Ky = (2*y2 + y1) / 3

Plugging in the values of L and R:

1. Kx = (2*1 - 5) / 3 = (-3) / 3 = -1
2. Ky = (2*2 - 1) / 3 = (3) / 3 = 1

Therefore, the coordinates of point K are (-1, 1).