Question

What are the coordinates of the point on the directed line segment from (-8, -2)(−8,−2) to (1, 10)(1,10) that partitions the segment into a ratio of 2 to 1?

Answer 1

The coordinates of the point that divides the line segment from (-8, -2) to (1, 10) in the ratio of 2 to 1 are (-2, 6), as calculated using the section formula in coordinate geometry.

Step-by-step explanation:

The coordinates of the point that partition the line segment from (-8, -2) to (1, 10) into a ratio of 2 to 1 can be found using the section formula in coordinate geometry. Given the partition ratio of m:n, where m=2 and n=1, the coordinates (x, y) of the dividing point P can be found using:

x = (mx2 + nx1) / (m + n)

y = (my2 + ny1) / (m + n)

Substituting the given points and values into the formula:

x = (2*1 + 1*(-8)) / (2 + 1) = (-6) / 3 = -2

y = (2*10 + 1*(-2)) / (2 + 1) = 18 / 3 = 6

So, the partitioning point's coordinates are (-2, 6).