Astudent wants to find point c on the directed line segment from a to b on a number line such that the segment is partitioned in a ratio of 3: 4. point a is at -6 and point b is at 2. the student's work is shown .

The point C directed line segment from A to B is -18/7.

Given that,

A student wants to find point C on the directed line segment from A to B on a number line such that the segment is partitioned in a ratio of 3:4.

Point A is at -6 and point B is at 2.

We have to determine,

The point C on the directed line segment from A to B.

According to the question,

Let, the distance AC be x,

And BC = 8 - x

The ratio of AC : BC = 3 : 4

Therefore,

Solving the equation by cross multiplication,

Then,

Point C directed line segment from A to B is,

Hence, The point C directed line segment from A to B is -18/7.

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Point C at (-18/7)

Step-by-step explanation:

Point A is at -6 and point B is at 2.

So, the distance between A and B = 2 - (-6) = 8

point C on the directed line segment from A to B on a number line such that the segment is partitioned in a ratio of 3:4.

Let the distance AC = x

∴ BC = 8 - x

AC : CB = 3 : 4

∴

Using cross multiplication

3 (8-x) = 4x

24 - 3x = 4x

24 = 7x

x = 24/7

So, Point C = -6 + 24/7 = -18/7

Point C at (-18/7)

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.