Question

In triangles ABC and DEF, the coordinates for A are (0, 1), for B are (0, 2), and for C are (3, 2). Given that ΔABC ≅ ΔDEF, what is the length of segment line FE rounded to the nearest tenth?

1) 3
2) 4
3) 1.1
4) 3.2

Answer 1

To find the length of segment line FE in ΔABC ≅ ΔDEF, we calculate the length of one side of ΔABC and use it as a reference. The length of BC is 3 units based on its coordinates, thus the length of FE is also 3 units because the triangles are congruent.

Step-by-step explanation:

To determine the length of segment line FE in triangles ABC and DEF where ΔABC ≅ ΔDEF, we must first calculate the length of one of the sides of ΔABC to use as a reference, since the triangles are congruent. The coordinates for A are (0, 1), for B are (0, 2), and for C are (3, 2). The length of segment line BC can be found by using the distance formula, which is the square root of the sum of the squares of the differences between the x-coordinates and the y-coordinates of the points B and C. Since B and C have the same y-coordinate, the length of BC is just the difference in the x-coordinates, which is 3 - 0 = 3. Therefore, the length of BC is 3 units. Since ΔABC ≅ ΔDEF, the length of segment line FE must also be 3 units.