Transformations are crucial part of maths. Rotation is a kind of transformation in which the geometrical shape of figure does not change. The measures of its dimensions remain the same and so properties like perimeter, area etc. In rotation shape and particularly its coordinates are rotated from one location to another by some angle with respect to reference axis. Let us see what is the formula for a triangle rotated 90 degrees counter clockwise.
When a triangle is rotated by 900, all of its 3 vertices are rotated by 900 in actual. So, the formula we follow for finding the new coordinates can be derived as:
Suppose we have a triangle with following coordinates initially: (-4, 0), (4, 0) and (0, 4), then on rotating it by an angle of 900 we see that original figure becomes:
Figure colored yellow is the original figure and one after rotation has been colored black.
The new coordinates can be found as follows:
If the original coordinate is of the form (x, y), then new coordinate after rotation would become: (- y, x).
So, original coordinates become:
(-4, 0) = (0, -4)
(4, 0) = (0, 4) and
(0, 4) = (-4, 0)
Thus our new coordinates are: (0, -4), (0, 4) and (-4, 0). Thus all the three vertices will be rotated by 900. Rotation does not change the shape of figure.
These are the coordinates when we are rotating the triangle counter clock – wise. If we compare the areas and perimeters of the two Triangles, we would find them identical. Thus we see that two triangles are congruent to each other. Measure of the sides of 1st triangle is “a” and same is for rotated triangle too.