Find the distance between two points

Learning Objectives Identify and plot points on a coordinate plane using ordered pairs. Calculate the horizontal and vertical distances between two points. Apply the Pythagorean theorem to find the diagonal distance between two points. Derive and use the distance formula to find the distance between any two points. Solve real-world problems involving the distance between two points on a coordinate plane. Ever wonder how far apart two cities are on a map, or how long a diagonal path is across a park? 🗺️ In this lesson, we'll learn how to measure these distances using math! You'll discover how to use the coordinate plane, the Pythagorean theorem, and a special formula to find the exact distance between any two points. This skill is super useful for understanding maps,...

TermDefinitionExample Coordinate PlaneA two-dimensional surface formed by two perpendicular number lines, the x-axis and y-axis, used to locate points.Imagine a grid where you can pinpoint any location using two numbers. Ordered PairA pair of numbers $(x, y)$ that represents the location of a point on the coordinate plane, where $x$ is the horizontal position and $y$ is the vertical position.The point $(3, 5)$ means you move 3 units right from the origin and 5 units up. x-coordinateThe first number in an ordered pair $(x, y)$, indicating the horizontal distance from the y-axis.In $(4, -2)$, the x-coordinate is 4. y-coordinateThe second number in an ordered pair $(x, y)$, indicating the vertical distance from the x-axis.In $(4, -2)$, the y-coordinate is -2. OriginThe point where the x-axis...

Horizontal Distance Formula $d = |x_2 - x_1|$ Use this formula to find the distance between two points that share the same y-coordinate. $x_1$ and $x_2$ are the x-coordinates of the two points. Vertical Distance Formula $d = |y_2 - y_1|$ Use this formula to find the distance between two points that share the same x-coordinate. $y_1$ and $y_2$ are the y-coordinates of the two points. Pythagorean Theorem $a^2 + b^2 = c^2$ This theorem relates the lengths of the legs ($a$ and $b$) of a right triangle to the length of its hypotenuse ($c$). We can use it to find the diagonal distance between two points by forming a right triangle. Distance Formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ This formula calculates the straight-line distance between any two points $...