Recall that two shapes are said to be congruent if the lengths of the sides and the angles are the same.
For triangle A B C to be congruent to triangle D E F, then A B = D E, A C = D F and B C = E F
Also, the triangle D E F is a result of a rigid body translation of the triangle A B C.
Given that A is at point (1, 0) and D is at point (-1, 0), also given that B is at point (-1, 2) and E is at point (1, -2).
It can be seen that points D E is a result of refrecting points A B
across the y-axis and then the x-axis.
Thus, given point C as (2, 3),
refrection of point C across the y-axis will result in point (-2,
3) and then reflecting the resulting point across the x-axis will
result to point (-2, -3).
Therefore, the coordinate for 'F' that would make triangle A B C and triangle D E F congruent is (-2, -3).
