Follow directions on a coordinate plane

Learning Objectives Interpret directional language (e.g., 'right,' 'left,' 'up,' 'down') in the context of a coordinate plane. Accurately locate a new point on the coordinate plane after a single translation from a given starting point. Determine the new coordinates of a point after a sequence of horizontal and vertical movements. Graphically represent the path of a point as it follows a series of directions. Identify the change in x and y coordinates corresponding to given directional movements. Apply directional instructions to solve problems involving geometric translations. Ever tried to give someone directions to a hidden treasure? 🗺️ It's all about clear instructions and understanding how to move! In this lesson, you'l...

TermDefinitionExample Coordinate PlaneA two-dimensional plane formed by the intersection of a horizontal number line (x-axis) and a vertical number line (y-axis).Imagine a city map laid out on a grid, where every location has a unique address. Ordered PairA pair of numbers (x, y) that specifies the exact location of a point on a coordinate plane. The first number is the x-coordinate, and the second is the y-coordinate.The point (3, -2) is 3 units right of the origin and 2 units down. OriginThe point (0, 0) where the x-axis and y-axis intersect. It serves as the starting point for all coordinate measurements.The center of a crosshairs target or the 'home' position on a robot's path. X-axisThe horizontal number line on the coordinate plane. Movement along this axis correspond...

Horizontal Movement Rule To move a point $(x, y)$ horizontally: - 'Right $a$ units': $(x, y) \rightarrow (x + a, y)$ - 'Left $a$ units': $(x, y) \rightarrow (x - a, y)$ Horizontal movements (left or right) only affect the x-coordinate. Moving right increases the x-value, while moving left decreases it. The y-coordinate remains unchanged. Vertical Movement Rule To move a point $(x, y)$ vertically: - 'Up $b$ units': $(x, y) \rightarrow (x, y + b)$ - 'Down $b$ units': $(x, y) \rightarrow (x, y - b)$ Vertical movements (up or down) only affect the y-coordinate. Moving up increases the y-value, while moving down decreases it. The x-coordinate remains unchanged. Combined Movement Rule To move a point $(x, y)$ by $a$ units horizontally...