Question

What are the coordinates of the point on the directed line segment from (-8, 9) to (-6, -3) that partitions the segment into a ratio of 3 to 1?

Answer 1

The coordinates of the point that divides the line segment from (-8, 9) to (-6, -3) in a 3 to 1 ratio are (-6.5, 0).

Step-by-step explanation:

The question asks for the coordinates of a point that divides the line segment between (-8, 9) and (-6, -3) into a ratio of 3 to 1. To find this point, we can apply the section formula or the concept of internal division, which states that the coordinates of a point dividing a line segment into a proportion a:b can be found by:

• [(ax2 + bx1) / (a + b), (ay2 + by1) / (a + b)]

In this case, a is 3 and b is 1, so:

• x-coordinate = [(3*-6) + (1*-8)] / (3+1) = (-18 - 8) / 4 = -26/4 = -6.5
• y-coordinate = [(3*-3) + (1*9)] / (3+1) = (-9 + 9) / 4 = 0/4 = 0

Therefore, the coordinates of the point are (-6.5, 0).