To find the new coordinates of point B' after a translation of (x-2,y+3), you add or subtract the corresponding values from the original coordinates of point B.
Original coordinates of B: (4,3)
Translation rule: (x-2, y+3)
To find the new x-coordinate of B', subtract 2 from the original x-coordinate of B:
New x-coordinate of B' = 4 - 2 = 2
To find the new y-coordinate of B', add 3 to the original y-coordinate of B:
New y-coordinate of B' = 3 + 3 = 6
Therefore, the coordinates for B' after the translation will be (2,6).
For the second question, to reflect a point across the x-axis, you keep the x-coordinate the same but change the sign of the y-coordinate:
Original coordinates of G: (3,-2)
After reflecting G across the x-axis, the new coordinates will be (3, -(-2)) = (3, 2).
Therefore, the coordinate for G after it is reflected across the x-axis is (3, 2).
For the third question, to find the translation rule that describes the composition of (x, y) --> (x+4, y-1) and (x, y) --> (x-5, y-5), you need to combine the two translation rules into one.
First translation rule: (x, y) --> (x+4, y-1)
Second translation rule: (x, y) --> (x-5, y-5)
To combine these two rules, you add the x-translations and the y-translations:
New x-translation = (4 + -5) = -1
New y-translation = (-1 + -5) = -6
Therefore, the translation rule that describes the composition of the two given rules is (x, y) --> (x-1, y-6).