Question

To create an image of rectangle ABCD that is translated 6 units to the right and 3 units up, you can apply these transformations to each vertex of the original rectangle. Here's how you can plot the corresponding vertices:

A(0, 0) remains unchanged.
B(0, 4) shifts 6 units to the right and 3 units up, becoming B'(6, 7).
C(4, 4) shifts 6 units to the right and 3 units up, becoming C'(10, 7).
D(4, 0) shifts 6 units to the right and 3 units up, becoming D'(10, 3).

Answer 1

To accurately translate rectangle ABCD by 6 units right and 3 units up, the translation vector is added to each vertex's coordinates, resulting in A'(6, 3), B'(6, 7), C'(10, 7), and D'(10, 3). The student's original description incorrectly left point A unchanged.

Step-by-step explanation:

To create an image of rectangle ABCD that is translated 6 units to the right and 3 units up from the original rectangle, you would apply the translation to each vertex of ABCD. When translating a point in the coordinate system, you add the translation vector to each coordinate. While vertex A(0, 0) does not move, vertex B(0, 4) should be translated to B'(6, 7), C(4, 4) to C'(10, 7), and D(4, 0) to D'(10, 3). However, the provided information includes an error, as A(0, 0) should indeed be shifted to become A'(6, 3) according to the described translation.

The translation involves adding the horizontal displacement to the x-coordinate and the vertical displacement to the y-coordinate. In more general terms, if a point is at (x, y), and it is translated by (dx, dy), the translated point would be at (x + dx, y + dy).