Question

The vertices of a rectangle are A(2,0), B(5,0), C (5,-2), and D(2,-2). Translate this rectangle 2 units left and 4 units up. Graph this.

Answer 1

To translate the rectangle, alter each vertex's coordinates accordingly: A'(0,4), B'(3,4), C'(3,2), and D'(0,2), and then plot these new vertices and connect them to graph the new rectangle position.

Step-by-step explanation:

To translate the rectangle with vertices A(2,0), B(5,0), C(5,-2), and D(2,-2) 2 units left and 4 units up, apply the translation to each vertex:

1. For A(2,0), moving 2 units left changes the x-coordinate from 2 to 0. Moving 4 units up changes the y-coordinate from 0 to 4. So, translated vertex A' will be at (0,4).
2. For B(5,0), moving 2 units left changes the x-coordinate from 5 to 3. Moving 4 units up changes the y-coordinate from 0 to 4. Therefore, translated vertex B' will be at (3,4).
3. For C(5,-2), moving 2 units left changes the x-coordinate from 5 to 3. Moving 4 units up changes the y-coordinate from -2 to 2. Thus, the translated vertex C' will be at (3,2).
4. For D(2,-2), moving 2 units left changes the x-coordinate from 2 to 0. Moving 4 units up changes the y-coordinate from -2 to 2. Consequently, translated vertex D' will be at (0,2).

To graph the translated rectangle, plot the new vertices A'(0,4), B'(3,4), C'(3,2), and D'(0,2) on a coordinate plane and draw straight lines connecting them in sequence to form the rectangle.