Question

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. The student's work is shown .

Answer 1

Answer:

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

∴$\frac{AC}{CB} =\frac{3}{4} = \frac{x}{8-x}$

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)

Answer 2

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,

$\dfrac{AC}{BC} = \dfrac{3}{4} = \dfrac{x}{8-x}$

Solving the equation by cross multiplication,

$3 (8-x) = 4x\\\\24 - 3x = 4x\\\\24 = 7x\\\\x = \dfrac{24}{7}$

Then,

Point C directed line segment from A to B is,

$= -6 + \dfrac{24}{7}\\\\= \dfrac{-42+24}{7}\\\\= \dfrac{-18}{7}$

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

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