Question

A point Q on a segment with endpoints A(2, −1) and C(4, 2) partitions the segment in a 3:1 ratio. Find Q.

Answer 1

Using proportions, it is found that the coordinates of Q are given as follows: (3.5, 1.25).

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Since the point Q partitions the segment AC in a 3:1 ratio, we have that the equation is:

$Q - A = \frac{3}{4}(C - A)$

For the x-coordinate, we have that:

$Q - A = \frac{3}{4}(C - A)$

$x - 2 = \frac{3}{4}(4 - 2)$

$x - 2 = \frac{3}{2}$

x = 3.5

For the y-coordinate, we have that:

$Q - A = \frac{3}{4}(C - A)$

$y + 1 = \frac{3}{4}(2 - (-1))$

$y + 1 = \frac{9}{4}$

y = 1.25.

The coordinates of Q are given as follows: (3.5, 1.25).

More can be learned about proportions at brainly.com/question/24372153

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