Question

in the coordinate plane, the point a (2, 0) is translated to the point a’(1, −4). under the same translation, the points b(6, 2) and c(4, −4) are translated to b’ and c’, respectively. what are the coordinates of b’ and c’?

Explanation:

Answer:

To find the translation vector, we calculate the change in \( x \)-coordinates and \( y \)-coordinates from \( A(2, 0) \) to \( A'(1, -4) \).

For the \( x \)-coordinate: \( 1 - 2 = -1 \) (so we shift left by 1 unit).
For the \( y \)-coordinate: \( -4 - 0 = -4 \) (so we shift down by 4 units).

Coordinates of \( B' \):

Given \( B(6, 2) \), apply the translation:

• New \( x \)-coordinate: \( 6 + (-1) = 5 \)
• New \( y \)-coordinate: \( 2 + (-4) = -2 \)

Thus, \( B' = (5, -2) \).

Coordinates of \( C' \):

Given \( C(4, -4) \), apply the translation:

• New \( x \)-coordinate: \( 4 + (-1) = 3 \)
• New \( y \)-coordinate: \( -4 + (-4) = -8 \)

Thus, \( C' = (3, -8) \).

Final answers:
\( B' = \boldsymbol{(5, -2)} \)
\( C' = \boldsymbol{(3, -8)} \)