Question

for questions 1-10 find the distance to the nearest hundredth.

Answer 1

The formula to find the distance, d, between two points is

$d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}$

Taking (1,1) as the coordinates of the first point and (4,5) as the coordinates of the second point as shown below,

$\begin{gathered} (x_1,y_1)\Rightarrow(1,1) \\ (x_2,y_2)\Rightarrow(4,5)_{} \end{gathered}$

Substitute the coordinates into the formula for the distance between two points

$\begin{gathered} d=\sqrt[]{(4-1)^2+(5-1)^2} \\ d=\sqrt[]{3^2+4^2} \\ d=\sqrt[]{9+16} \\ d=\sqrt[]{25} \\ d=5\text{ units} \end{gathered}$

Hence, the distance between the two points is 5 units