Question

What coordinate for F would make triangle ABC and triangle DEF congruent? Triangle ABC is shown. For triangle ABC, A is at 0, 3, B is at negative 1, 2, C is at 2, 3. Two other coordinates are shown. D is at negative 1, 0, E is at 1, negative 2. (−3,−3) (−3,−2) (−2,−3) (−2,−2)

Answer 1

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).