Question

Triangle ABC is translated to image A′B′C′. In this translation, A(5, 1) maps to A′(6, –2). The coordinates of B′ are

(–1, 0). What are the coordinates of B?

Answer 1

We know that point A(5, 1) maps to A'(6, -2) in the translation. To find the translation vector, we can subtract the coordinates of A from the coordinates of A':

Translation vector = A' - A = (6, -2) - (5, 1) = (1, -3)

This means that every point in the preimage moves 1 unit to the right and 3 units down to reach its corresponding point in the image.

We also know that point B'(−1, 0) is the image of a point B in the preimage. To find the coordinates of point B, we can apply the translation vector to B':

B = B' - Translation vector = (-1, 0) - (1, -3) = (-2, 3)

Therefore, the coordinates of point B in the preimage are (-2, 3).