The Distance Formula
Apply the distance formula in Grade 9 math — It calculates the direct, straight-line distance between any two points by creating a right triangle from the
Key Concepts
Property The distance $d$ between two points $(x 1, y 1)$ and $(x 2, y 2)$ is $$d = \sqrt{(x 2 x 1)^2 + (y 2 y 1)^2}$$.
Explanation Think of this formula as the Pythagorean theorem's cool cousin for coordinates! It calculates the direct, straight line distance between any two points by creating a right triangle from the coordinate differences and finding its hypotenuse. It's a secret map shortcut!
Examples Find the distance between $(3, 2)$ and $(6, 4)$: $d = \sqrt{(6 3)^2 + (4 ( 2))^2} = \sqrt{3^2 + 6^2} = \sqrt{45} = 3\sqrt{5}$. Find the distance between $( 1, 7)$ and $(4, 5)$: $d = \sqrt{(4 ( 1))^2 + ( 5 7)^2} = \sqrt{5^2 + ( 12)^2} = \sqrt{169} = 13$.
Common Questions
What is 'The Distance Formula' in Grade 9 math?
It calculates the direct, straight-line distance between any two points by creating a right triangle from the coordinate differences and finding its hypotenuse. Find the distance between $(-1, 7)$ and $(4, -5)$: $d = \sqrt{(4 - (-1))^2 + (-5 - 7)^2} = \sqrt{5^2 + (-12)^2} = \sqrt{169} = 13$.
How do you solve problems involving 'The Distance Formula'?
Find the distance between $(-1, 7)$ and $(4, -5)$: $d = \sqrt{(4 - (-1))^2 + (-5 - 7)^2} = \sqrt{5^2 + (-12)^2} = \sqrt{169} = 13$. The Distance Formula is your secret weapon for finding the exact distance between any two points on a graph.
Why is 'The Distance Formula' an important Grade 9 math skill?
Remember the order of operations (PEMDAS)!. You must calculate the values inside the parentheses, then square them, then add, and finally take the square root.