Question

What coordinate for f would make triangle abc and triangle def congruent? triangle abc is shown. for triangle abc, a is at 1, 0, 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, 2. (−2, 4) (−2, 3) (−3, 3) (−3, 4)

Answer 1

The coordinate that would make triangles ABC and DEF congruent is F at (-2, 3), by ensuring each point on triangle DEF is a mirror image of triangle ABC across the y-axis.

Step-by-step explanation:

To determine which coordinate for point F would make triangles ABC and DEF congruent, we must ensure that all corresponding sides and angles of the triangles are identical. Let's examine triangle ABC provided, where A is at (1, 0), B is at (-1, 2), and C is at (2, 3). We've also been given points D and E for triangle DEF, which are (-1, 0) and (1, 2), respectively.

By comparing, we notice that points A and D are both one unit away from the y-axis, and similarly, points B and E are mirrors of each other with respect to the y-axis as well. For the coordinate of F to make both triangles congruent, it must also be symmetrical to point C across the y-axis. Point C is located one unit to the right of the y-axis and three units above point B. Therefore, point F should be located one unit to the left of the y-axis and three units above point D. Thus, point F should be at (-2, 3).

To confirm that point F at (-2, 3) is correct, we apply the Pythagorean theorem, a² + b² = c², to calculate the lengths of the sides of triangle ABC and the corresponding sides of triangle DEF, ensuring they match.