Coordinates

Summary

Exercises

From standard coordinates to perpframe coordinates.

Here's a perpframe together with the point

Use a matrix hit to find numbers a and b so that .

(The numbers a and b are the perpframe coordinates of the point P.)

Answer: You can get the numbers a and b by hitting the point P with the .
Let P and the check the plot.

With a and b defined as above you see that .

Why does that work?

Answer: Here's what you get when you hit everything in the plot above with the aligner matrix: [Graphics:coordinatesgr9.gif]

The location of the rotated point aligner.P relative to the xy-axis

is the same as

the location of the original point P relative to the perpframe.

But in this picture it's clear that the numbers a and b should be the x and y coordinates of the point aligner.P.

From perpframe coordinates to standard coordinates.

For the perpframe shown below, use a matrix hit to find the xy-coordinates of the point P that has perpframe coordinates {-2,3}. [Graphics:coordinatesgr10.gif]

Answer: The column method for matrix multiplication tells you that the standard xy-coordinates of the point P are given by

Summary

A hit with the aligner matrix takes standard coordinates to perpframe coordinates.
A hit with the hanger matrix takes perpframe coordinates to standard coordinates.

Exercises

1. Estimate by eye the

coordinates of the point P shown in the plot below.

2. In terms of and express a matrix M so that M P gives the coordinates of the point P.

Todd Will UW-La Crosse

Coordinates

From standard coordinates to perpframe coordinates.

From perpframe coordinates to standard coordinates.

Summary

Exercises

Todd Will
UW-La Crosse