Question

Appy the Pythagorean theorem to find the distance between two points in a coordinator system

Answer 1

From the given figure

There is a line with 2 endpoints (4, 5) and (-3, -3)

We need to find the two sides of the right triangle formed from the line and the vertical, horizontal lines

The vertical side = 8 squares

The horizontal line = 7 squares

Then the 2 legs of the triangle are 8 and 7

We will use the Pythagorean relation to find the length of the line (the hypotenuse of the triangle)

`h=\sqrt[]{(l_1)^2+(l_2)^2}`

Let l1 = 8 and l2 = 7, then

`\begin{gathered} h=\sqrt[]{(8)^2+(7)^2} \\ h=\sqrt[]{64+49} \\ h=\sqrt[]{113} \end{gathered}`

The distance between the two given points is

`\sqrt[]{113}`