Question

In the coordinate plane, the point A (4, 0) is translated to the point A'(0, 2). Under the same translation, the points B (7. - 4) and C(6. -3) are translated to B' and C', respectively. What are the coordinates of B' and C'?​

Answer 1

To translate points B and C in the same way as A was translated to A', subtract 4 from the x-coordinates and add 2 to the y-coordinates. This gives B' (3, -2) and C' (2, -1).

Step-by-step explanation:

To find the coordinates of B' and C' after the translation of points in the coordinate plane, you need to determine the change that occurred when point A was translated to A'. The change in the x-coordinate is Ax' - Ax = 0 - 4 = -4, and the change in the y-coordinate is Ay' - Ay = 2 - 0 = 2.

Applying the same change to points B (7, -4) and C (6, -3), we get the following:

• Bx' = Bx - 4 = 7 - 4 = 3
• By' = By + 2 = -4 + 2 = -2
• Cx' = Cx - 4 = 6 - 4 = 2
• Cy' = Cy + 2 = -3 + 2 = -1

Therefore, the new coordinates after the translation are B' (3, -2) and C' (2, -1).