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.