Chapter 13: Q. 16 (page 526)

Given points A, B, and C. Find AB, BC, and AC. Are A, B, and C collinear?
If so, which point lies between the other two?
16. A(3, 4), B(-3, 0), C(-1, 1)

Short Answer

Expert verified

The values of $A B = 2 \sqrt{13}, B C = \sqrt{5}, A C = 5$ .

A, B, Care not collinear.

Step by step solution

Step-1 – Given

The given points are $A (3, 4), B (- 3, 0), C (- 1, 1)$ .

Step-2 – To determine

We have to find the lengths AB, BCand AC.Then have to check ifA, B, C are collinear. And determine that which point lies between the other two.

Step-3 – Calculation

Using the distance formula, the distance between A and B is:

$\begin{array}{l} A B = \sqrt{{(- 3 - 3)}^{2} + {(0 - 4)}^{2}} \\ A B = \sqrt{{(- 6)}^{2} + {(- 4)}^{2}} \\ A B = \sqrt{36 + 16} \\ A B = \sqrt{52} \\ A B = 2 \sqrt{13} \end{array}$

Using the distance formula, the distance between B and C is:

$\begin{array}{l} B C = \sqrt{{(- 1 - (- 3))}^{2} + {(1 - 0)}^{2}} \\ B C = \sqrt{{(- 1 + 3)}^{2} + {(1 - 0)}^{2}} \\ B C = \sqrt{{(2)}^{2} + {(1)}^{2}} \\ B C = \sqrt{4 + 1} \\ B C = \sqrt{5} \end{array}$

Using the distance formula, the distance between A and C is:

$\begin{array}{l} A C = \sqrt{{(- 1 - 3)}^{2} + {(1 - 4)}^{2}} \\ A C = \sqrt{{(- 4)}^{2} + {(- 3)}^{2}} \\ A C = \sqrt{16 + 9} \\ A C = \sqrt{25} \\ A C = 5 \end{array}$

Note that the sum of any two lines is not equal to length of other line.

So, A, B, Care not collinear.

The values of $A B = 2 \sqrt{13}, B C = \sqrt{5}, A C = 5$ .

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Given points A, B, and C. Find AB, BC, and AC. Are A, B, and C collinear?
If so, which point lies between the other two?
16. A(3, 4), B(-3, 0), C(-1, 1)

Short Answer

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

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Given points A, B, and C. Find AB, BC, and AC. Are A, B, and C collinear?If so, which point lies between the other two?16. A(3, 4), B(-3, 0), C(-1, 1)

Short Answer

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Probability and Statistics

Decision Maths

Pure Maths

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Given points A, B, and C. Find AB, BC, and AC. Are A, B, and C collinear?
If so, which point lies between the other two?
16. A(3, 4), B(-3, 0), C(-1, 1)