Find k so that the distance from (–3, –1) to (k, 5) is 10 units.

There are two solutions for : 5 and -11.

In this case, we must use the Length Equation for Line Segment to solve for , whose formula is described below:

(1)

Where:

- Coordinates of the initial endpoint.

- Coordinates of the final endpoint.

- Length of the line segment.

If we know that , and , then the equation is expanded into this form:

The roots of this Second Order Polynomial are determined by Quadratic Formula:

or .

There are two solutions for : 5 and -11.

Please see this related question: link

k = - 11, 5

Step-by-step explanation:

By distance formula: