Finding the Shortest Distance on the Coordinate Plane using the Pythagorean Theorem

This lesson teaches how to find the length of a line segment on a coordinate plane using the Pythagorean theorem. It reviews the theorem, explains common mistakes, and provides examples of calculating distances between points and the shortest distance between two houses. The lesson concludes with a summary of the key concepts covered.

What is the formula used in the Pythagorean theorem to find the length of the hypotenuse?

• a² + b² = c²

• a² - b² = c²

• a² + b² = 2c²

• a² = b² + c²

When finding the distance between two points, why is it incorrect to simply count the spaces between them?

• Because the spaces are too large

• Because the spaces are too small

• Because the units are not visible

• Because the spaces are not always equal

In the example of finding the distance between points A(-5, -6) and B(-2, 4), what is the length of the longer leg of the right triangle formed?

• 5 units

• 10 units

• 4 units

• 3 units

What is the calculated distance between points A(-5, -6) and B(-2, 4) after applying the Pythagorean theorem?

• 5 units

• 10.4 units

• 12 units

• 15.8 units

In the final example, what is the shortest distance between the two houses after rounding to the nearest tenth?

• 15.8 units

• 14.2 units

• 13.5 units

• 16.0 units