To verify: The point M is equidistant from the vertices of triangle ABC.
Explanation of Solution
Given information:
The point M is the midpoint of the line segment AB and figure,
Formula used:
Mid-point formula between two points
Distance formula between two points
Proof:
Consider the given figure,
In the above figure, M is the mid-point of the line segment AB.
Recall the mid-point formula between two points
So, coordinates of point M will be calculated as,
Now, to show that M is equidistant from the vertices of triangle ABC, prove that the distance from point M to the vertices are equal, i.e.,
Recall the distance formula between two points
So, distance between A and M is calculated as,
Distance between B and M is calculated as,
Distance between C and M is calculated as,
Since,
Thus, it is proved that point M is equidistant from the vertices of triangle ABC.
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning