Question

A segment with endpoints A (3, 2) and B (6, 11) is partitioned by a point C such that AC and BC form a 2:3 ratio. Find the x value for C.

3.8

3.9

4.2

4.3

Answer 1

First we subtract x values of points A and B
|3-6| = 3

now because the ration is 2:3 we need to divide that distance with 5 (sum of ratio numbers)
3/5

The result we multiply by 2 and add to x value of point A because that is the order of our ration (AC/BC)

2*3/5+3 = 4.2

Answer is 4.2

Answer 2

The x-coordinate of the point C within a line segment between points A(x, y) = (3, 2) and B(x, y) = (6, 11) and an AC to BC ratio of 2 : 3 is equal to 4.2.

How to find the coordinates of a point within a line segment

In this question we must apply concepts of ratios, line segments and vector sum to determine the coordinates of a point:

C(x, y) = A(x, y) + k · [B(x, y) - A(x, y)]     (1)

Where k is the ratio of the point C.

If we know that A(x, y) = (3, 2) and B(x, y) = (6, 11), then the coordinates of the point C are:

C(x, y) = (3, 2) + (2/5) · [(6, 11) - (3, 2)]

C(x, y) = (3, 2) + (2/5) · (3, 9)

C(x, y) = (4.2, 5.6)

The x-coordinate of the point C within a line segment between points A(x, y) = (3, 2) and B(x, y) = (6, 11) and an AC to BC ratio of 2 : 3 is equal to 4.2.

To learn more on line segments: https://brainly.com/question/25727583

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