Question

What are the coordinates of the point on the directed line segment from (-6, -6)(−6,−6) to (9, -1)(9,−1) that partitions the segment into a ratio of 2 to 3?

Answer 1

(0, -4)

Explanation:

The coordinates of the points from which the directed line segment extends = (-6, -6) to (9, -1)

The ratio the required point partitions the line = 2 to 3

The formula for finding the coordinate of a point that partitions a line AB into a ratio 'a' to 'b', where the coordinates of, A = (x₁, y₁) and B = (x₂, y₂) is given as follows;

`\left((a)/(a + b) * (x_1 - x_2)+ x_1, \ (a)/(a + b) * (y_1 - y_2)+ y_1 \right)`

Therefore, the required point is located as follows;

`\left((2)/(2 + 3) * (9 - (-6))+ (-6), \ (2)/(2 + 3)* (-1 - (-6))+ (-6) \right) = (0, -4)`

The coordinates of the point is (0, -4)