Question

If rectangle ABDC is translated horizontally −1 and vertically +3, which of the following correctly depicts rectangle A′B′D′C′ ?

Answer 1

To translate rectangle \(ABCD\) horizontally by \(-1\) (to the left) and vertically by \(+3\) (upwards), you will adjust the coordinates of each vertex of the rectangle accordingly.

Assuming the original coordinates of the rectangle \(ABCD\) are as follows:
- A \((x_A, y_A)\)
- B \((x_B, y_B)\)
- C \((x_C, y_C)\)
- D \((x_D, y_D)\)

The new coordinates after the translation to obtain vertices \(A'B'D'C'\) will be:
- \(A' (x_A - 1, y_A + 3)\)
- \(B' (x_B - 1, y_B + 3)\)
- \(C' (x_C - 1, y_C + 3)\)
- \(D' (x_D - 1, y_D + 3)\)

This means you will reduce the x-coordinate of each vertex by \(1\) and increase the y-coordinate by \(3\).

To depict the new rectangle \(A'B'D'C'\), simply take each vertex of the original rectangle, apply the translations, and plot the new points on a coordinate plane. This will result in a rectangle that is shifted left by \(1\) unit and up by \(3\) units from its original position.