Answer:
[tex]B(x,y) = (-2,-4)[/tex]
[tex]O(x,y) = (6,-6)[/tex]
[tex]Y(x,y) = (13,1)[/tex]
Step-by-step explanation:
Given
[tex]Translation: (-3,6)[/tex]
[tex]B': (-5,2)[/tex]
[tex]O':(3,0)[/tex]
[tex]Y': (10,7)[/tex]
Required
Determine the coordinates of B, O and Y
Recall that the given translation is:
[tex](x,y) = (-3,6)[/tex]
Calculating the x coordinates of B:
[tex]B_x + x = B'_x[/tex]
Where [tex]B': (-5,2)[/tex]
This gives
[tex]B_x -3 = -5[/tex]
[tex]B_x = -5 + 3[/tex]
[tex]B_x = -2[/tex]
Calculating the y coordinates of B:
[tex]B_y + y = B'_y[/tex]
This gives
[tex]B_y + 6 = 2[/tex]
[tex]B_y = 2 - 6[/tex]
[tex]B_y = -4[/tex]
Hence:
[tex]B(x,y) = (-2,-4)[/tex]
Calculating the x coordinates of O:
[tex]O_x + x = O'_x[/tex]
Where [tex]O':(3,0)[/tex]
This gives
[tex]O_x -3 = 3[/tex]
[tex]O_x = 3 + 3[/tex]
[tex]O_x = 6[/tex]
Calculating the y coordinates of O:
[tex]O_y + y = O'_y[/tex]
This gives
[tex]O_y + 6 = 0[/tex]
[tex]O_y = 0 - 6[/tex]
[tex]O_y = - 6[/tex]
Hence:
[tex]O(x,y) = (6,-6)[/tex]
Calculating the x coordinates of Y:
[tex]Y_x + x = Y'_x[/tex]
Where [tex]Y': (10,7)[/tex]
This gives
[tex]Y_x -3 = 10[/tex]
[tex]Y_x = 10 + 3[/tex]
[tex]Y_x = 13[/tex]
Calculating the y coordinates of Y:
[tex]Y_y + y = Y'_y[/tex]
This gives
[tex]Y_y + 6 = 7[/tex]
[tex]Y_y = 7 - 6[/tex]
[tex]Y_y = 1[/tex]
Hence:
[tex]Y(x,y) = (13,1)[/tex]
