Question

Given the points (2,k) and (0,−6), for which values of k would the distance between the points be 5–√ ?

Answer 1

The value of k are -5 and -7 if the distance between points (2,k) and (0,−6) is √5

What is a distance formula?

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

$\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The question is:

Given the points (2,k) and (0,−6), for which values of k would the distance between the points be √5

$\rm \sqrt{5}=\sqrt{(0-2)^2+(-6-k)^2}$

5 = 4 + (6 + k)²

After solving:

$\rm 4+\left(6+k\right)^2-4=5-4$

(6 + k)² = 1

k = -5 or -7

Thus, the value of k are -5 and -7 if the distance between points (2,k) and (0,−6) is √5

Learn more about the distance formula here:

brainly.com/question/18296211

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