116k views
4 votes
What are the coordinates of the point on the directed line segment from (- 2, -2) to (9, 9) that partitions the segment into a ratio of 5 to 6?

1 Answer

5 votes

Answer:

Step-by-step explanation:

The coordinates of the point that partitions the line segment from (-2, -2) to (9, 9) into a ratio of 5 to 6 is the point (5.5, 5.5).

To find the coordinates of this point, we need to use the formula for the midpoint of a line segment:

Midpoint = (x1 + x2)/2, (y1 + y2)/2

In this case, x1 = -2, x2 = 9, y1 = -2, y2 = 9.

Therefore, the midpoint = (-2 + 9)/2, (-2 + 9)/2

Substituting the values:

Midpoint = (7/2, 7/2)

Since the midpoint has to be in the ratio of 5 to 6, we divide each of the components of the midpoint by 11/6:

Midpoint = (7/2)/(11/6), (7/2)/(11/6)

Simplifying:

Midpoint = (15/22, 15/22)

Therefore, the coordinates of the point that partitions the line segment from (-2, -2) to (9, 9) into a ratio of 5 to 6 is the point (5.5, 5.5).

User Steve Coleman
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories