Finding Distances

How can you use the Pythagorean Theorem to find the distance between any two points on a dot grid?

How can you use it to find the end points of a line with a length of square root of 13?

Refer to the grid for questions A-D.  Click the virtual geoboard button below the grid to create your right triangles.

Part A

1. Copy the points above onto your virtual geoboard.  Then, draw a right triangle with segment KL as its hypotenuse.

2. Find the lengths of the legs of the triangle.

3. Use the Pythagorean Theorem to find the length of segment KL.

Part B

Find the distance between points M and N by connecting them with a segment and using the method in Part A.

Part C

Find the distance between points P and Q.

Part D

In the beginning of this Unit, you found the driving distance between the stadium at (-2,3) and the high school at (1,8).  What is the helicopter distance between these two locations?  Estimate the difference of the two distances.

Part E

Find the coordinates of two points that are square root of 13 units apart.  Label the points R and S.  Explain how you know the distance between the points is square root of 13 units?