Question

Find the distance between A and B.OA. 8 unitsOB. 4√5 unitsOC. 4√3 unitsOD. 10 units

Answer 1

Step 1

Write the coordinates of A and B.

A(-4, 2) and B(4, -2)

Step 2

Apply the distance between two points formula

`\begin{gathered} D_(AB)\text{ = }√((x_2-x_1)^2+(y_2-y_1)^2) \\ \\ x_1\text{ = -4, y}_1=\text{ 2, x}_2\text{ = 4, y}_2\text{ = -2} \\ \\ D_(AB)\text{ =}√((4-(-4))^2+(-2-2)^2) \end{gathered}`

Next, simplify further

`\begin{gathered} D_(AB)\text{ = }√((4+4)^2+(-4)^2) \\ \\ D_(AB)\text{ = }√(64+16) \\ \\ D_(AB)\text{ = }√(80) \\ \\ D_(AB)\text{ = }\sqrt{16\text{ }*5} \\ \\ D_(AB)\text{ = 4}√(5) \end{gathered}`

Final answer

`\begin{gathered} Option\text{ B} \\ 4\sqrt{5\text{ }}\text{ units} \end{gathered}`