Question

What are the coordinates of the point on the directed line segment from (-4,-1) to (6,4) that partitions the segment into a ratio of 3 to 2?

Answer 1

Using proportions, it is found that the coordinates of the desired point are (2,2).

• The first point is A(-4, -1).

• The second point is B(6, 4).

• The desired point is C(x,y).

The point C partitions the segment AB into a ratio of 3 to 2, hence:

$C - A = \frac{3}{5}(B - A)$

This proportion is applied using both the x and y coordinates of the points, hence:

$x - (-4) = \frac{3}{5}[6 - (-4)]$

$x + 4 = 6$

$x = 2$

$y - (-1) = \frac{3}{5}[4 - (-1)]$

$y + 1 = 3$

$y = 2$

The coordinates of the desired point are (2,2).

To learn more about proportions, you can take a look at brainly.com/question/4854238