Coordinate Plane
Distance Formula
How does the distance formula show the Pythagorean Theorem?
5 Problems - SHOW ALL WORK!
Plot the points:
A: (1,-3) B: (7,5) C: (-2,-1) D: (-8,5)
Draw a line connecting points A and B and then points C and D. Estimate the distance between the two points.
AB ______ CD _______
Connect the points using a horizontal and vertical line to create a right triangle with legs that represent the horizontal and vertical distance between the points.
Use the Pythagorean Theorem to find the length of AB and CD in problem 1.
Use the Pythagorean Theorem to find the missing lengths.
Find the length of the line.
In your own words, how can the Pythagorean Theorem be used to find the distance between two points on the coordinate plane?
1. AB = √((7-1)^2 + (5-(-3))^2) = √(6^2 + 8^2) = √(36 + 64) = √100 = 10
CD = √((-8-(-2))^2 + (5-(-1))^2) = √((-6)^2 + 6^2) = √(36 + 36) = √72
2. Estimate:
AB ≈ 10 units
CD ≈ √72 units
3. Using the Pythagorean Theorem:
AB = √((7-1)^2 + (5-(-3))^2) = √(6^2 + 8^2) = √100 = 10 units
CD = √((-8-(-2))^2 + (5-(-1))^2) = √((-6)^2 + 6^2) = √(36 + 36) = √72 units
4. The length of the line connecting the two points is √72 units.
5. The Pythagorean Theorem can be used to find the distance between two points on the coordinate plane by treating the horizontal and vertical distances between the two points as the legs of a right triangle. The distance formula derived from the Pythagorean Theorem can then be applied to calculate the length of the hypotenuse, which represents the distance between the two points.