triangle ABC has vertices at A(1,-3),B(3,0), and C(5,-3). what is the distance from vertex B to the midpoint of AC

The distance from vertex B to the midpoint of AC is 3.

Step-by-step explanation:

From Linear Algebra we understand that location of the midpoint of AC is determined by the following formula:

(1)

Where:

, - Locations of vertices A and C regarding origin, dimensionless.

- Location of the midpoint regarding origin, dimensionless.

If we know that and , then the midpoint of AC is:

Lastly, the distance from vertex B to the midpoint of AC is calculated from the Pythagorean Theorem:

(2)

If we know that , , and , then the distance is:

The distance from vertex B to the midpoint of AC is 3.

46.2+112.3

step-by-step explanation: