Question

Jarvis wants to translate rectangle ABDC horizontally by -4 and vertically by +3 to produce rectangle A'B'D'C'. What will be the coordinates of C' after Jarvis completes this translation?
Coordinates of ABDC: A(-5,4), B(-1,4), D( -1,1), C(-5,1)

Answer 1

To translate rectangle ABDC horizontally by -4 and vertically by +3, we need to apply the translation to each vertex's coordinates. The translation can be expressed as follows:

- Horizontal translation: \(x' = x - 4\)
- Vertical translation: \(y' = y + 3\)

Now let's find the coordinates of point C, which is given as \(C(-5, 1)\).

1. Apply the horizontal translation:
\[
x' = -5 - 4 = -9
\]

2. Apply the vertical translation:
\[
y' = 1 + 3 = 4
\]

Thus, after applying both translations, the new coordinates \(C'\) will be:
\[
C'(-9, 4)
\]

Therefore, the coordinates of C' after the translation are \(\boxed{(-9, 4)}\).