Question

In the coordinate plane, the point A (1,2) is translated to the pointA’ (6,3). Under the same translation, the pointsB (- 3,5) and C ( -2,6) are translated to B’ and C’

respectively. What are the coordinates of and ?

Answer 1

After applying the same translation that moved point A to A', point B is translated to B' (2,6) and point C to C' (3,7).

Step-by-step explanation:

To find the coordinates of points B' and C' after the translation that moved point A (1,2) to A' (6,3), we need to apply the same change to points B and C.

First, we calculate the changes in the x and y coordinates from A to A':

• Change in x (Δx) = x-coordinate of A' - x-coordinate of A = 6 - 1 = 5
• Change in y (Δy) = y-coordinate of A' - y-coordinate of A = 3 - 2 = 1

Now, we apply these changes to points B and C to find B' and C':

• B' = (Δx + x-coordinate of B, Δy + y-coordinate of B) = (5 - 3, 1 + 5) = (2, 6)
• C' = (Δx + x-coordinate of C, Δy + y-coordinate of C) = (5 - 2, 1 + 6) = (3, 7)

Therefore, the coordinates of points B' and C' after the translation are (2, 6) and (3, 7) respectively.