Question

Find the distance between (–3, –3) and (6, 12). Round the answer to the nearest hundredth, if necessary.

Answer 1

`(-3, -3), \ \ (6, 12)\\ \\distance \ formula : \\ \\d =\sqrt{(x_(2)-x_(1))^2 +(y_(2)-y_(1))^2} \\ \\d =√((6-(-3))^2 +(12-(-3) )^2) =√((6+3)^2 +(12+3 )^2) =√(9^2+15^2)=\\ \\=√(81+225)=√(306)=√(9\cdot 34)=3√(34)=3\cdot 5.83= 17.49`

Answer 2

`A=(x_A;y_A)\ \ \ and\ \ \ B=(x_B;y_B)\\\\ \Rightarrow\ \ \ |AB|= √((x_A-x_B)^2+(y_A-y_B)^2) \\----------------------\\\\A=(-3;-3);\ \ \ B=(6;12)\\\\|AB|= √((-3-6)^2+(-3-12)^2) =\\\\.\ \ \ \ \ \ = √(81+225) = √(306) =3 √(34) \approx17.49`