SOLUTION: please help me solving this problem.perform a 45 degree rotation of atriangle A(0,0),B(1,1),C(5,2) (a)about the origin and(b)about p(-1,-1).
Algebra ->
Coordinate-system
-> SOLUTION: please help me solving this problem.perform a 45 degree rotation of atriangle A(0,0),B(1,1),C(5,2) (a)about the origin and(b)about p(-1,-1).
Log On
Question 1137113: please help me solving this problem.perform a 45 degree rotation of atriangle A(0,0),B(1,1),C(5,2) (a)about the origin and(b)about p(-1,-1). Answer by Theo(13342) (Show Source):
theta is the rotation angle, which in your problem would be 45 degrees.
x and y are the original (x,y) coordinates.
x' and y' are the rotated coordinates.
if you are rotating about the origin, you use the formulas directly on the old coordinates.
if you are rotating about a point that is not the origin, like the point (-1,-1), you need to translate the old coordinates by subtracting the coordinates of the rotation point from them and then use the formulas on the translated coordinates.
when you are don, you need to then translate back by adding the coordinates of the rotation point to them.
this is all shown in the attached spreadsheet that does the required translations and applies the formulas to the translated coordinates and then translates back.
i then graphed the old points and the new points to see what they would look like.
i have 2 graphs.
the first rotates about the origin and the second rotates about the point (-1,-1).
i verified through the use of excel and the length of a line between two points formula that the lengths of the original sides of the triangle and the length of the rotated sides of the triangle were the same, as they should have been.
