Question

Point G is rotated 90°. The coordinate of the pre-image point G was (7, –5), and its image G’ is at the coordinate (5, 7). What is the direction of the rotation?
A. counter-clockwise
B. horizontally
C. symmetrical
D. clockwise

Answer 1

Answer:

D.Clockwise

Step-by-step explanation:

90 Degree Rotation

When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.

Your progress isn't being saved! Log in or Sign up to save future progress.

Search for courses, skills, and videos

Main content

Rotations

Rotating shapes about the origin by multiples of 90°

Learn how to draw the image of a given shape under a given rotation about the origin by any multiple of 90°.

Introduction

In this article we will practice the art of rotating shapes. Mathematically speaking, we will learn how to draw the image of a given shape under a given rotation.

This article focuses on rotations by multiples of 90^\circ90∘90, degrees, both positive (counterclockwise) and negative (clockwise).

Part 1: Rotating points by 90^\circ90∘90, degrees, 180^\circ180∘180, degrees, and -90^\circ−90∘minus, 90, degrees

Let's study an example problem

We want to find the image A'A′A, prime of the point A(3,4)A(3,4)A, left parenthesis, 3, comma, 4, right parenthesis under a rotation by 90^\circ90∘90, degrees about the origin.

Let's start by visualizing the problem. Positive rotations are counterclockwise, so our rotation will look something like this:

yyxxA'A′\blueD{A(3,4)}A(3,4)

Cool, we estimated A'A′A, prime visually. But now we need to find exact coordinates. There are two ways to do this.

Solution method 1: The visual approach

We can imagine a rectangle that has one vertex at the origin and the opposite vertex at AAA.

\small{1}1\small{2}2\small{3}3\small{4}4\small{5}5\small{6}6\small{7}7\small{8}8\small{9}9\small{\llap{-}2}-2\small{\llap{-}3}-3\small{\llap{-}4}