Question

Triangle ABC has coordinates A(2,6), B(2,0), and C(7,0). If Triangle DEF has coordinates D(2,-2) and E(2,-8), then what must be the coordinates of F to make the two triangles congruent?

Answer 1

The coordinates of point F to make the two triangles congruent must be F(7,-8).

To make triangles ABC and DEF congruent, corresponding vertices must have the same relative positions. In this case, points A and D already share the same x-coordinate (2), and points B and E share the same x-coordinate (2) as well.

However, to complete the congruence, point F must have the same coordinates as point C. Since point C has coordinates (7, 0), the coordinates of point F need to be (7, -8) to ensure that the triangles ABC and DEF are congruent. This maintains the relative positions of the vertices and satisfies the conditions for congruence.