Associated Topics || Dr. Math Home || Search Dr. Math

### Rotating a Point

```Date: 04/08/2003 at 09:19:04
From: Reggie
Subject: Coordinates on a grid

What is the formula for figuring out the coordinates to answer a
question like:

Find the image of a triangle with vertices A(0,1),B(-2,0) and
C(-4,-5) under a rotation of 90 degrees counterclockwise about the
origin.

Is there a formula I can use instead of drawing a picture?
```

```
Date: 04/08/2003 at 12:42:55
From: Doctor Rick
Subject: Re: Coordinates on a grid

Hi, Reggie.

Yes, there is, but I suggest that you graph one point anyway. You can
discover the formula by examining how the coordinates of that one
point change under this rotation. Then you can apply the same formula
to the other points.

Take any one of the points - I suggest C, because it's not on either
axis - and find the coordinates of the rotated point. Hint: You can
rotate the point by turning the whole page counterclockwise 90
degrees.

y                                x
^                                ^
|                                |
|                                |
|                                |
-4     |                                |      -5
-----+-----+--------->x  ===>  y<-----------+-------+----
:     |                                |       :
:     |                                |       :
:     |                              -4+.......*
*.....+-5                              |
|                                |

Then relabel the axes the right way. You want to rotate the point but
NOT the axes.

y
^
|
|
|
|       5
------------+-------+---->x
|       :
|       :
-4+.......*
|
|

What was the positive x-axis is now pointing up, so it is where the
positive y-axis should be. Therefore, what was the x-coordinate is
now the y-coordinate. On the other hand, what was the positive y-axis
is now the NEGATIVE x-axis. It is pointing left. How is the new
x-coordinate related to the old y-coordinate?

coordinates of the rotated point, but a rule for changing the old
coordinates to the new coordinates. This rule could be applied to any
point.

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Euclidean/Plane Geometry
High School Symmetry/Tessellations

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search