Question

Perform a 45 degree rotation of triangle a(0 0) b(1 1) c(5 2) about origin

Answer 1

In rotation of points about the origin through 45 degrees, we can use either construction method or the formula

x1= xcos(45∘)−ycos(45∘)

y1= xsin(45∘)+ycos(45∘)

 

In this solution, we have used the above formula, and we assume that the rotation is counter-clockwise,

A(0,0)  will be mapped on A1(0, 0)

B (1, 1) will be mapped on B1(0, 1.4)

 C(5, 2) will be mapped on C1(2.1, 4.9) 

 

See the attached figure

Answer 2

We can find the coordinates of the triangle without necessarily drawing.

We can follow the following steps.

1. Representing the given triangle in matrix form using homogeneous coordinates of the vertices.

2. Identifying the matrix of rotation of 45°.

3. Applying the concept of trigonometric ratios. That is cos 45° = Sin45° = √2/2

4. Getting the rotated triangle A'B'C' by multiplying the matrix of triangle ABC and the matrix of rotation.

Find calculations and further details in the image.