Question

If three distinct points $A, B,$ and $C$ in $a$ plane are such that the slopes of nomvertical line segments $A B, A C,$ and $B C$ are equal, then $A, B,$ and $C$ are collinear: Otherwise, they are not. Use this fact to determine whether the three points given are collinear. $$ (-1,-3),(-5,12),(1,-11) $$

Name: Problem 77, Chapter 2: College Algebra and Trigonometry
Uploaded: 2021-08-28T16:19:01-08:00
Duration: 1 min 19 s
Channel: Erika Bustos
Description: If three distinct points A, B, and C in a plane are such that the slopes of nomvertical line segments A B, A C, and B C are equal, then A, B, and C are collinear: Otherwise, they are not. Use this fact to determine whether the three points given are collinear. (-1,-3),(-5,12),(1,-11)

   If three distinct points $A, B,$ and $C$ in $a$ plane are such that the slopes of nomvertical line segments $A B, A C,$ and $B C$ are equal, then $A, B,$ and $C$ are collinear: Otherwise, they are not. Use this fact to determine whether the three points given are collinear.
$$
(-1,-3),(-5,12),(1,-11)
$$

College Algebra and Trigonometry

Margaret L. Lial,… 7th Edition

Chapter 2, Problem 77

Instant Answer

Solved by Expert Erika Bustos

08/28/2021

Step 1

The formula for the slope of a line segment between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\frac{y_2 - y_1}{x_2 - x_1}$. Show more…

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If three distinct points $A, B,$ and $C$ in $a$ plane are such that the slopes of nomvertical line segments $A B, A C,$ and $B C$ are equal, then $A, B,$ and $C$ are collinear: Otherwise, they are not. Use this fact to determine whether the three points given are collinear. $$ (-1,-3),(-5,12),(1,-11) $$

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Key Concepts

Collinearity

Collinearity refers to the condition where three or more points lie on a single straight line. A key method for verifying collinearity is by comparing the slopes of line segments joining the points. If the slopes between any two pairs of points are equal, then all the points are collinear; if not, the points do not lie on the same line.

Slope of a Line

The slope of a line is a measure of its steepness and is calculated as the ratio of the change in the y-coordinates to the change in the x-coordinates between any two points. It is a fundamental concept in coordinate geometry that helps describe the direction and inclination of lines in the plane.

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