Question

Triangle ABC is translated according to the rule (x, y) → (x + 2, y – 8). If the coordinates of the pre-image of point B are
(4, –5), what are the coordinates of B'?

(2, 3)
(1, –9)
(–3, –4)
(6, –13)

Answer 1

To find the coordinates of point B' after the translation of triangle ABC, we need to apply the given translation rule to the coordinates of point B.

The translation rule is given as:
\((x, y) \rightarrow (x + 2, y - 8)\).

The coordinates of the pre-image of point B are:
\((4, -5)\).

Now we can apply the translation rule:

1. For the x-coordinate:
\[
x' = 4 + 2 = 6
\]

2. For the y-coordinate:
\[
y' = -5 - 8 = -13
\]

Putting these together, the coordinates of point B' after the translation are:
\((6, -13)\).

Thus, the coordinates of B' are \((6, -13)\). Therefore, the correct answer is:

**(6, -13)**.