Question

Find the distance between the points (4,5) and (2, 2). Show as much work as you can.Graph the line segment on the coordinate plane

Answer 1

√13 units.

Step-by-step explanation:

To find the distance between any two points, use the distance formula below:

`Distance=√((x_2-x_1)^2+(y_2-y_1)^2)`

Given the points as:

`\begin{gathered} (x_1,y_1)=(4,5) \\ \mleft(x_2,y_2\mright)=\mleft(2,2\mright) \end{gathered}`

Substitute the points into the formula:

`\begin{gathered} Distance=\sqrt[]{(2-4)^2+(2-5)^2} \\ =\sqrt[]{(-2)^2+(-3)^2} \\ =\sqrt[]{4+9} \\ =\sqrt[]{13} \end{gathered}`

The distance between the two points is √13 units.

The graph is attached below:

Note: √13 is approximately 3.61 units (to 2 decimal places).