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Question

A rectangle is labeled upper A upper B upper C upper D. Vertices upper A and upper B are labeled as follows: upper A equals left parenthesis negative 5 comma 4 right parenthesis, and upper B equals left parenthesis negative 1 comma 4 right parenthesis.

If square ABDC is translated 2 units to the left and 4 units down to produce square A′B′D′C′ , what are the coordinates of B′ ?

Answer 1

To find the coordinates of point \( B' \) after the translation, we start with the original coordinates of point \( B \), which are given as \( B = (-1, 4) \).

The translation involves moving the point:

• 2 units to the left, which means we subtract 2 from the x-coordinate.
• 4 units down, which means we subtract 4 from the y-coordinate.

Applying the translation to the coordinates of \( B \):

• New x-coordinate: \( -1 - 2 = -3 \)
• New y-coordinate: \( 4 - 4 = 0 \)

Therefore, the coordinates of \( B' \) after the translation are:

\[ B' = (-3, 0) \]