Pythagorean Theorem on a Grid
Learn pythagorean theorem on a grid in Grade 9 math — Explanation Tired of moving in L-shapes on a map? Part of Quadratic Functions and Equations for Grade 9.
Key Concepts
Property To find the direct distance (hypotenuse $c$) on a grid, use the horizontal distance ($a$) and vertical distance ($b$) as the triangle's legs in the Pythagorean Theorem: $a^2 + b^2 = c^2$.
Explanation Tired of moving in L shapes on a map? The Pythagorean theorem is your express route! Just count the blocks you move sideways and the blocks you move up or down. Those two numbers become the legs of a right triangle, letting you solve for the shortcut distance.
Examples A car travels 4 blocks east and 3 blocks north. The direct distance is $\sqrt{4^2 + 3^2} = \sqrt{16+9} = \sqrt{25} = 5$ blocks. A bug crawls 8 cm right and 6 cm down. The direct distance from start to finish is $\sqrt{8^2 + 6^2} = \sqrt{64+36} = \sqrt{100} = 10$ cm.
Common Questions
What is 'Pythagorean Theorem on a Grid' in Grade 9 math?
Explanation Tired of moving in L-shapes on a map? The Pythagorean theorem is your express route!.
How do you solve problems involving 'Pythagorean Theorem on a Grid'?
The Pythagorean theorem is your express route! Just count the blocks you move sideways and the blocks you move up or down.
Why is 'Pythagorean Theorem on a Grid' an important Grade 9 math skill?
Always remember to square each leg separately first, then add the squared numbers together.. The hypotenuse is always shorter than $a+b$!.