Transformation matrices graph the image

Learning Objectives Identify the original shape (pre-image) and the transformed shape (image) on a coordinate plane. Understand that a 'transformation matrix rule' provides specific instructions for changing coordinates. Apply transformation matrix rules (like translation and reflection) to find the new coordinates of points. Plot the new coordinates to accurately graph the image of a shape after a transformation. Describe the type of transformation (e.g., translation, reflection) given a set of coordinate changes. Connect transformation rules to two-variable equations that describe how coordinates change. Have you ever moved furniture around a room or seen a reflection in a mirror? 🛋️✨ In math, we can 'move' shapes on a graph too! In this lesson, you&#...

TermDefinitionExample Coordinate PlaneA flat surface made up of two perpendicular number lines, the x-axis (horizontal) and the y-axis (vertical), used to locate points with ordered pairs.Plotting the point (3, 2) means moving 3 units right from the origin and 2 units up. Point (x, y)An ordered pair of numbers that shows the exact location of a point on the coordinate plane. The first number is the x-coordinate, and the second is the y-coordinate.The point (5, -1) is 5 units to the right of the y-axis and 1 unit below the x-axis. TransformationA mathematical process that moves or changes a geometric shape's position or orientation on a coordinate plane without changing its size or shape.Sliding a square to a new spot on the graph is a type of transformation called a translation. Pre-...

Translation Matrix Rule (Slide) $(x, y) \rightarrow (x + a, y + b)$ This rule, derived from a translation matrix, tells you to add 'a' to the x-coordinate and 'b' to the y-coordinate to slide the point. 'a' is the horizontal shift (right if positive, left if negative), and 'b' is the vertical shift (up if positive, down if negative). These are two-variable equations: $x' = x + a$ and $y' = y + b$. Reflection Matrix Rule (Flip across x-axis) $(x, y) \rightarrow (x, -y)$ This rule, derived from a reflection matrix, tells you to keep the x-coordinate the same and change the sign of the y-coordinate. This flips the point over the x-axis. The two-variable equations are: $x' = x$ and $y' = -y$. Reflection Matrix Rule...