Question

Triangle abc has coordinates a (3,3), b (0,0), and c (3,0). if the triangle is rotated 180 degrees about point b, what will be the coordinates of the images of a and c (a' and c')? write sentences describing your steps.

Answer 1

By plotting the given points in the co-ordinate plane, we observe that it forms a right angled triangle.

Now the line-segment BC is inclined at an angle of 45 degrees in the first quadrant. We are rotating that line by 180 degrees i.e. keep point B where it is and move the point A(3,3), then it will pass through the 2nd quadrant. It will still form a 45 degree angle, but in the 3rd quadrant. Therefore, the rotated point now has co-ordinates A' (-3, -3).

Now, for the line-segment BC. Again we keep point B where it is, and move point C (3,0) 180 degrees, then it will pass through the 1st and end up in the 2nd quadrant and point C will have the co-ordinates C' (-3, 0).

So, the points after rotation are A' (-3, -3) and C' (-3, 0)