Question

Given the points (–3,k)(–3,k) and (2,0)(2,0), for which values of k would the distance between the points be 34−−√34 ?

Answer 1

Answer:

The possible values of k are 3 and -3

Step-by-step explanation:

Given

Points: (-3,k) and (2,0)

Distance between them = √34

Required

Determine the value of k

The distance between two points is calculated as thus;

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

Let

$(x_1,y_1) = (-3,k)$

$(x_2,y_2) = (2,0)$

Substitute these values in the given formula

$Distance = \sqrt{(-3 - 2)^2 + (k - 0)^2}$

Evaluate the brackets

$Distance = \sqrt{-5^2 + k^2}$

$Distance = \sqrt{25 + k^2}$

Recall that Distance = √34

So; we have

$\sqrt{34} = \sqrt{25 + k^2}$

Take square of both sides

$34 = 25 + k^2$

Collect Like Terms

$k^2 = 34 - 25$

$k^2 = 9$

Take square root of both sides

$k = \±3$

Hence, the possible values of k are 3 and -3