Question

Determine the distance between A(-3, 4) and B(2, -4).

Answer 1

5 units

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}`

Let

P1=A(-3,4)

P2=B(2,-4)

Step 2

put the values into the equation

`\begin{gathered} \text{distance}=\sqrt[]{(-4-4)^2+(2-(-3))^2} \\ \text{distance}=\sqrt[]{(0)^2+(2+3)^2} \\ \text{distance}=\sqrt[]{(0)^2+(5)^2} \\ \text{distance}=\sqrt[]{(25} \\ \text{distance}=5 \end{gathered}`