Start your trial now! First week only $4.99!*arrow_forward*

BuyFind*launch*

6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.8, Problem 48E

To determine

**To verify: **The point M is equidistant from the vertices of triangle ABC.

Expert 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.