Question

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

Answer 1

The triangle ABC is translated 1 unit down and 3 units to the left to obtain triangle DEF with vertices D(-1,0), E(0,3), and F(-2,2).

Step-by-step explanation:

The student is asking about translating a triangle in a two-dimensional Cartesian coordinate system. When translating a figure in geometry, each vertex of the figure is moved the same distance in the same direction.

In this specific question, the vertices of triangle ABC are given, and we need to translate the triangle 1 unit down (which means subtracting 1 from the y-coordinate of each vertex) and 3 units to the left (subtracting 3 from the x-coordinate of each vertex).

To translate vertex A(2, 1), we subtract 3 from the x-coordinate and 1 from the y-coordinate, resulting in the new coordinates A'(2-3, 1-1) = A'(-1, 0). Similarly, for vertex B(3, 4), the translated coordinates are B'(3-3, 4-1) = B'(0, 3), and for vertex C(1, 3), they are C'(1-3, 3-1) = C'(-2, 2).

Therefore, the vertices of the translated triangle DEF are D(-1,0), E(0,3), and F(-2,2).

Answer 2

The new coordinates will be D(1,3) E(0,3) and F(-1,0)

Step-by-step explanation:

As can be seen in the picture, points A and B are moved one point negative in the y-axis, and three in the x-axis. Point C and D will have the same coordinates to form the new triangle.