Find the point (3,1) using the (blue, blue) coordinate system. What is it in (yellow, orange)? answer below
Find the point (1,2) using the (blue, blue) coordinate system. What is it in (yellow, orange)? answer below
A larger picture is provided so you can find more points. You will soon be taking data and then working to find the algebra behind the data.
The (yellow, orange) for (3,1) is (1,0) and (yellow, orange) for (1,2) is (0,1).
Now let’s work in the other direction. Find go from yellow-orange to blue-blue testing (2,0), (3,0), (4,0) and (0,2), (0,3), (0,4).
You get (6,2), (9,3), (12,4) and (2,4), (3,6), (4,8). You can see patterns.
Do one more, (2,2), (3,3), (4,4).
You get (4,3) for (1,1)
You get (8,6) for (2,2)
You probably guessed (12,9) for (3,3) and then confirmed it. There are different ways to get to the equations using the data and to cut to the chase we’ll provide the answer. You should do your own work to convince yourself of the following…
x’ = 3x + 1y
y’ = 1x + 2y
…where (x’,y’) is (yellow, orange) and (x,y) is (blue, blue). We are deliberately publishing factors of 1 to make it easier to see 3,1 and 1,2.
Vectoreverything 