Question

Given the points (–3,k) and (2,0), for which values of k would the distance between the points be √34 ?A. 2 or -6B. 5 or -6C. 5 or 0D. 3 or -3

Answer 1

The distance between points (x1, y1) and (x2, y2) is computed as follows:

`d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1_{})^2}`

Substituting with the points (–3,k) and (2,0) and d = √34, we get:

`\begin{gathered} \sqrt[]{34}=\sqrt[]{(2_{}-(-3))^2+(0-k)^2} \\ 34=5^2+k^2 \\ 34-25=k^2 \\ 9=k^2 \\ \sqrt[]{9}=k \\ \pm3=k \end{gathered}`

The distance would be √34 if the values of k are 3 or -3.