Question

For each exercise draw a grid and find the coordinates of the image point. 0 is the origin and $A$ is the point $(3,1) . R_{x}$ and $R_{y}$ are reflections in the $x$ - and $y$ -axes. $$ \mathscr{R}_{O, 90} \circ R_{y} :(-2,1) \rightarrow(\longrightarrow, (\underline{?}, \underline{?}) $$

Name: Problem 22, Chapter 14: Geometry
Uploaded: 2019-10-27T23:51:23-08:00
Duration: 7 s
Channel: Amrita Bhasin
Description: For each exercise draw a grid and find the coordinates of the image point. 0 is the origin and A is the point (3,1) . Rx and Ry are reflections in the x - and y -axes. ℛO, 90 ∘Ry :(-2,1) →(⟶, (?, ?)

   For each exercise draw a grid and find the coordinates of the image point.
0 is the origin and $A$ is the point $(3,1) . R_{x}$ and $R_{y}$ are reflections in the $x$ - and $y$ -axes. 
$$
\mathscr{R}_{O, 90} \circ R_{y} :(-2,1) \rightarrow(\longrightarrow, (\underline{?}, \underline{?})
$$

Geometry

Ray C.… 1st Edition

Chapter 14, Problem 22

Instant Answer

Solved by Expert Amrita Bhasin

10/27/2019

Step 1

The reflection in the y-axis changes the sign of the x-coordinate, so we get $(2,1)$. Show more…

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For each exercise draw a grid and find the coordinates of the image point. 0 is the origin and $A$ is the point $(3,1) . R_{x}$ and $R_{y}$ are reflections in the $x$ - and $y$ -axes. $$ \mathscr{R}_{O, 90} \circ R_{y} :(-2,1) \rightarrow(\longrightarrow, (\underline{?}, \underline{?}) $$

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Key Concepts

Composition of Transformations

This concept refers to the sequential application of multiple transformations. The overall transformation is found by applying each transformation step-by-step, where the output of one becomes the input for the next.

Rotation Transformation

Rotation in coordinate geometry turns a point around a fixed center (often the origin). For example, a 90-degree rotation around the origin transforms a point (x, y) into (-y, x) when rotating counterclockwise.

Reflection Transformation

A reflection in a line (e.g., the y-axis) in coordinate geometry maps a point to its mirror image across that line. Typically, reflecting a point (x, y) across the y-axis results in the point (-x, y).

Coordinate Geometry

This concept involves understanding the two-dimensional coordinate plane, where points are represented by pairs of numbers. It provides the framework for plotting and analyzing positions, grids, and geometric transformations.

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