Translations: find the coordinates

Learning Objectives Define translation as a geometric transformation. Identify the horizontal and vertical components of a translation. Apply translation rules to find the coordinates of a translated point. Determine the translation rule given a pre-image and its image. Translate geometric figures (e.g., triangles, quadrilaterals) on a coordinate plane. Distinguish between a pre-image and an image after a translation. Ever moved a piece on a chessboard without rotating or resizing it? ♟️ That's a translation! In this lesson, you'll learn how to describe these 'slides' mathematically using coordinates. We'll discover how to find the new position of any point or shape after it has been translated, which is a fundamental concept in geometry and essenti...

TermDefinitionExample TransformationA change in the position, size, or orientation of a geometric figure. Translations are one type of transformation.Sliding a square across a page, rotating a triangle, or reflecting a shape in a mirror. TranslationA transformation that 'slides' a figure from one position to another without turning it or changing its size. Every point of the figure moves the same distance in the same direction.Moving a point from (2,3) to (5,4) by sliding it 3 units right and 1 unit up. Pre-imageThe original figure or point before a transformation is applied.If point A is at (1,2) before being moved, A is the pre-image. ImageThe new figure or point after a transformation has been applied. It is often denoted with a prime symbol (e.g., A' for the image of A)...

Translation Rule for a Point $(x, y) \rightarrow (x+a, y+b)$ To translate a point $(x, y)$ by 'a' units horizontally and 'b' units vertically, add 'a' to the x-coordinate and 'b' to the y-coordinate. 'a' is positive for a shift to the right, negative for a shift to the left. 'b' is positive for a shift upwards, negative for a shift downwards. Finding the Translation Vector If $(x, y)$ is translated to $(x', y')$, then $a = x' - x$ and $b = y' - y$. The translation vector is $(a, b)$. To find the translation vector that moved a pre-image point $(x, y)$ to its image point $(x', y')$, subtract the original x-coordinate from the new x-coordinate to find the horizontal shift ('a'),...