Translations: find the coordinates

Learning Objectives Define a geometric translation as a slide on the coordinate plane. Identify the horizontal and vertical components of a translation rule. Apply a given translation rule to find the new coordinates of a single point. Apply a given translation rule to find the new coordinates of the vertices of a polygon. Determine the translation rule given the coordinates of a pre-image and its image. Accurately plot pre-image and image points on the coordinate plane after a translation. Have you ever rearranged furniture in your room, sliding a desk from one wall to another? 🛋️ That's a real-world translation! In this lesson, we'll explore how to describe these 'slides' mathematically on a coordinate plane. You'll learn how to find the exact ne...

TermDefinitionExample TranslationA transformation that 'slides' a figure from one position to another without rotating, reflecting, or resizing it. Every point of the figure moves the same distance in the same direction.Sliding a square 3 units to the right and 2 units up. Coordinate PlaneA two-dimensional plane formed by the intersection of a horizontal number line (x-axis) and a vertical number line (y-axis). Points are located using ordered pairs (x, y).The point (3, 2) is located 3 units right of the origin and 2 units up. Ordered PairA pair of numbers (x, y) that specifies the location of a point on a coordinate plane. The first number (x) indicates horizontal position, and the second number (y) indicates vertical position.For the point A(5, -1), 5 is the x-coordinate and -...

General Translation Rule $(x, y) \rightarrow (x+a, y+b)$ This rule describes how any point $(x, y)$ on the coordinate plane moves. 'a' represents the horizontal shift (positive for right, negative for left), and 'b' represents the vertical shift (positive for up, negative for down). You add 'a' to the x-coordinate and 'b' to the y-coordinate to find the new image coordinates. Horizontal Translation $(x, y) \rightarrow (x+a, y)$ This is a specific case of the general rule where only the x-coordinate changes. The figure slides left or right. 'a' is the horizontal shift. The y-coordinate remains unchanged. Vertical Translation $(x, y) \rightarrow (x, y+b)$ This is a specific case where only the y-coordinate changes. The...