Question

Find the distance d between 21 and 22.Express your answer in exact terms and simplify, if needed.d=ImCO876-543+2+1+orA++ ++-9 -8 -7 -6 -5 -4 -3 -2+ Re1 2 3 4 5 6 7 8 9Cnu-2 +-3+-4-5+-6+

Answer 1

From the graph provided, the coordinates of the two points are;

$\begin{gathered} z_1=(7,1) \\ z_2=(2,-7) \end{gathered}$

The distance between two points is;

$\begin{gathered} d=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ \text{Where;} \\ x_1=7,y_1=1,x_2=2,y_2=-7 \end{gathered}$

Then, we substitute the values into the formula, we have;

$\begin{gathered} d=\sqrt[]{(-7-1)^2+(2-7)^2} \\ d=\sqrt[]{(-8)^2+(-5)^2} \\ d=\sqrt[]{64+25} \\ d=\sqrt[]{89} \end{gathered}$

The distance d, between the points is;

$d=\sqrt[]{89}=9.4340$