Question

The vertices of triangle ABC are A(2, 1), B(3, 4), and C(1, 3). If triangle ABC is translated 1 unit down and 3 units to the left to create triangle DEF, what are the coordinates of the vertices of DEF?

a) D(0, -1), E(0, 3), F(-2, -2)
b) D(-1, 0), E(0, 3), F(-2, 2)
c) D(-2, -2), E(0, 3), F(-1, 0)
d) D(0, 1), E(1, 2), F(1, 3)

Answer 1

The coordinates of the vertices of triangle DEF, after translating triangle ABC 1 unit down and 3 units to the left, are D(-1, 0), E(0, 3), and F(-2, 2).

Step-by-step explanation:

To find the coordinates of the vertices of triangle DEF after a translation of triangle ABC, we will move each vertex of triangle ABC 1 unit down and 3 units to the left. This process is known as a geometric translation where the position of a shape is moved without changing its size, orientation, or shape.

The translation of vertex A(2, 1) means subtracting 1 from the y-coordinate and subtracting 3 from the x-coordinate, giving us D(-1, 0). Similarly, translating vertex B(3, 4) gives us E(0, 3), and translating vertex C(1, 3) results in F(-2, 2).

Therefore, the correct coordinates for the vertices of triangle DEF are:

• D(-1, 0)
• E(0, 3)
• F(-2, 2)