What are the coordinates of the point on the directed line segment from (-7, -10)(−7,−10) to (7, 4)(7,4) that partitions the segment into a ratio of 5 to 2?

Answer 1

In general, the coordinates of a point which partitions a directed line segment AB at the ratio of a:b from A(x₁, y₁) to B(x_2, y₂) is determined by the following formula:

(x, y) = (x₁ + (a/(a+b))(x₂-x₁), y₁ + (a/(a+b))(y₂-y₁).

Therefore, (-7 + (5/7)(7-(-7)), (-10 + (5/7)(4-(-10)))

(-7 + (5/7)(14), -10 + (5/7)(14))

(-7 + 10, -10 + 10)

(3, 0).