Question

If AABC = AEDF where the coordinates of A(0, 2), B(2, 4), and C(2, -1), what is the measure of DF?

A. 03
B. 03.1
C. 05
D. 0 5.9

Answer 1

To find the measure of side DF, we calculate the length of side BC using the distance formula. The length of side BC is 5 units, and since the triangles are congruent, the length of DF is also 5 units.

Step-by-step explanation:

If triangle ABC is congruent to triangle EDF (AABC = AEDF), and the coordinates of points A(0, 2), B(2, 4), and C(2, -1), we can calculate the measure of side DF by first finding the length of side BC because corresponding sides of congruent triangles are equal in length.

To find the length of side BC, we can use the distance formula:

1. Calculate the difference in the x-coordinates (x2 - x1), which is 2 - 2 = 0.
2. Calculate the difference in the y-coordinates (y2 - y1), which is -1 - 4 = -5.
3. Square both differences: 0^2 = 0, (-5)^2 = 25.
4. Add the squares: 0 + 25 = 25.
5. Take the square root of the sum to get the distance: sqrt(25) = 5.

So, the length of side BC is 5 units. Since triangle ABC is congruent to triangle EDF, the measure of DF is also 5 units.

Therefore, the measure of DF is 5 units, which corresponds to option C.