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.

To know more about Equation click the link given below.

link

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)