Question

The coordinates of the endpoints of overline LM are L(-8,7) and M(1,1). Point N is on overline LM and divides it such that LN:MN is 1:2

What is the product of the coordinates of N?
Write your answer as an integer or decimal.

Answer 1

To find the coordinates of point N on the line segment LM, we divide the segment in the ratio 1:2. The product of the coordinates of N is 2/9.

Step-by-step explanation:

To find the coordinates of point N, we need to divide the line segment LM in the ratio 1:2. This means that LN is one-third of the length of LM, and MN is two-thirds of the length of LM.

First, we find the length of LM using the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

d = sqrt((1 - (-8))^2 + (1 - 7)^2)

d = sqrt(9^2 + (-6)^2)

d = sqrt(81 + 36)

d = sqrt(117)

d = 10.82 (approximately)

Next, we find the coordinates of point N by multiplying the x and y coordinates of point M by the ratios: 1/3 for x and 2/3 for y.

xN = 1 * (1/3) = 1/3

yN = 1 * (2/3) = 2/3

Therefore, the product of the coordinates of point N is (1/3) * (2/3) = 2/9.