Question

Determine the distance between M(4, 0) and N(-2, -3).

Answer 1

`\text{distance = }\sqrt[]{45}`

Step-by-step explanation

Step 1

the distance between 2 points P1 and P2 is given by:

`\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where} \\ P1(x_1,y_1)andP2(x_2,y_2) \end{gathered}`

Step 2

let

P1=M(4,0)

P2=N(-2,-3)

replace

`\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{distance}=\sqrt[]{(-2-4)^2+(-3-0)^2} \\ \text{distance}=\sqrt[]{(-6)^2+(-3)^2} \\ \text{distance}=\sqrt[]{36+9} \\ \text{distance}=\sqrt[]{45} \\ \end{gathered}`

I hope this helps you