Question

Line segment ab has endpoints a(2, 5) and b(6, 2). Find the coordinates of the point that divides the line segment directed from a to b in the ratio of 1:2.

1) (4, 10)
2) (10, 4)
3) (16, 7)
4) (7, 16)

Answer 1

To find the coordinates of the point that divides the line segment ab in the ratio of 1:2, we can use the section formula. None of the provided options are correct.

Step-by-step explanation:

To find the coordinates of the point that divides the line segment from a(2, 5) to b(6, 2) in the ratio of 1:2, we can use the section formula. The section formula states that the coordinates of a point P that divides the line segment AB in the ratio m:n are given by:

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

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

Using the given values m = 1 and n = 2, we can substitute the values and calculate:

x = (1 * 6 + 2 * 2) / (1 + 2) = 2

y = (1 * 2 + 2 * 5) / (1 + 2) = 4

Therefore, the coordinates of the point that divides the line segment in the ratio of 1:2 is (2, 4), which is not included in the given options. None of the provided options are correct.