Coordinate plane (Review)

Learning Objectives Plot ordered pairs and identify the four quadrants. Calculate the distance between two points using the Distance Formula. Find the midpoint of a line segment using the Midpoint Formula. Calculate the slope of a line from two points or an equation. Write the equation of a line in slope-intercept and point-slope forms. Determine if two lines are parallel, perpendicular, or neither by comparing their slopes. Ever wonder how your phone's GPS knows the shortest route or how video game characters move across the screen? 🗺️ It all starts with the coordinate plane! This tutorial will refresh your skills with the coordinate plane, including plotting points, finding distance and slope, and writing linear equations. Mastering these fundamentals is crucial for...

TermDefinitionExample Ordered Pair (x, y)A pair of numbers used to locate a point on a plane, where 'x' is the horizontal coordinate and 'y' is the vertical coordinate.The point P(3, -4) is located 3 units to the right of the origin and 4 units down. QuadrantsThe four regions into which the x-axis and y-axis divide the coordinate plane. They are numbered I, II, III, and IV, starting from the top right and moving counter-clockwise.A point with a negative x-coordinate and a positive y-coordinate, like (-2, 5), is in Quadrant II. Slope (m)A measure of the steepness of a line, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.A line passing through (0,0) and (2,4) has a slope of m = (4-0)/(2-0) = 2. For...

Distance Formula d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} Used to find the straight-line distance between two points (x₁, y₁) and (x₂, y₂). This formula is derived from the Pythagorean theorem. Midpoint Formula M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) Used to find the exact center point of a line segment connecting points (x₁, y₁) and (x₂, y₂). It calculates the average of the x-coordinates and the average of the y-coordinates. Slope Formula m = \frac{y_2 - y_1}{x_2 - x_1} Used to calculate the slope (m) of a line passing through points (x₁, y₁) and (x₂, y₂). It represents the 'rise over run'. Slope-Intercept Form y = mx + b A common form for a linear equation where 'm' is the slope and 'b' is the y-intercept....