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?
To find the distance between two points on the coordinate plane using the Pythagorean Theorem, we can first draw a right triangle with the horizontal and vertical distances as the legs of the triangle. Then, we can use the formula a^2 + b^2 = c^2, where a and b represent the lengths of the legs of the triangle and c represents the length of the hypotenuse. By substituting the horizontal and vertical distances as a and b, we can solve for c, which represents the distance between the two points.
answer each question
1. Using the Pythagorean Theorem for AB:
AB = √((7-1)^2 + (5-(-3))^2)
AB = √(6^2 + 8^2)
AB = √(36 + 64)
AB = √100
AB = 10
2. Using the Pythagorean Theorem for CD:
CD = √((-8-(-2))^2 + (5-(-1))^2)
CD = √((-6)^2 + 6^2)
CD = √(36 + 36)
CD = √72
3. Connecting the points to form a right triangle:
Using the Pythagorean Theorem, we find:
CD = √((7-(-8))^2 + (5-(-1))^2)
CD = √(15^2 + 6^2)
CD = √(225 + 36)
CD = √261
4. In your own words, how can the Pythagorean Theorem be used to find the distance between two points on the coordinate plane?
The Pythagorean Theorem can be used to find the distance between two points on the coordinate plane by considering the horizontal and vertical distances between the points as the legs of a right triangle. By applying the Pythagorean Theorem formula a^2 + b^2 = c^2, where a and b are the lengths of the legs and c is the length of the hypotenuse (distance between the two points), we can solve for the missing length. This method calculates the shortest distance between the two points.