The Pythagorean Theorem on the Coordinate Plane
The Pythagorean Theorem on the Coordinate Plane is a Grade 8 math skill from Big Ideas Math, Course 3, Chapter 7: Real Numbers and the Pythagorean Theorem. Students apply the Pythagorean Theorem to find the distance between two points by treating the horizontal and vertical distances as the legs of a right triangle, leading to the Distance Formula d = sqrt((x2-x1)^2 + (y2-y1)^2). This skill bridges geometry and coordinate algebra.
Key Concepts
The distance, $d$, between two points $(x 1, y 1)$ and $(x 2, y 2)$ on a coordinate plane is found by applying the Pythagorean Theorem. This results in the Distance Formula: $$d = \sqrt{(x 2 x 1)^2 + (y 2 y 1)^2}$$.
Common Questions
How is the Pythagorean Theorem used on the coordinate plane?
The horizontal and vertical distances between two points form the legs of a right triangle, and the distance between the points is the hypotenuse, found using the Pythagorean Theorem.
What is the Distance Formula?
The Distance Formula is d = sqrt((x2-x1)^2 + (y2-y1)^2), which directly applies the Pythagorean Theorem to find the straight-line distance between two coordinate points.
How do you find the distance between two points on a coordinate plane?
Subtract the x-coordinates and square the result, subtract the y-coordinates and square the result, add those two values, then take the square root.
Where is the Pythagorean Theorem on the coordinate plane taught in Grade 8?
Big Ideas Math, Course 3, Chapter 7: Real Numbers and the Pythagorean Theorem covers this skill in the Grade 8 curriculum.