Question

Given △ B O Y has been transformed under the translation: T − 3 , 6 to form image at B′ ( − 5,2 ) , O′ ( 3,0 ) , Y′ ( 10,7 ) . Find the coordinates of the preimage.

Answer 1

`B(x,y) = (-2,-4)`

`O(x,y) = (6,-6)`

`Y(x,y) = (13,1)`

Explanation:

Given

`Translation: (-3,6)`

`B': (-5,2)`

`O':(3,0)`

`Y': (10,7)`

Required

Determine the coordinates of B, O and Y

Recall that the given translation is:

`(x,y) = (-3,6)`

Calculating the x coordinates of B:

`B_x + x = B'_x`

Where
`B': (-5,2)`

This gives

`B_x -3 = -5`

`B_x = -5 + 3`

`B_x = -2`

Calculating the y coordinates of B:

`B_y + y = B'_y`

This gives

`B_y + 6 = 2`

`B_y = 2 - 6`

`B_y = -4`

Hence:

`B(x,y) = (-2,-4)`

Calculating the x coordinates of O:

`O_x + x = O'_x`

Where
`O':(3,0)`

This gives

`O_x -3 = 3`

`O_x = 3 + 3`

`O_x = 6`

Calculating the y coordinates of O:

`O_y + y = O'_y`

This gives

`O_y + 6 = 0`

`O_y = 0 - 6`

`O_y = - 6`

Hence:

`O(x,y) = (6,-6)`

Calculating the x coordinates of Y:

`Y_x + x = Y'_x`

Where
`Y': (10,7)`

This gives

`Y_x -3 = 10`

`Y_x = 10 + 3`

`Y_x = 13`

Calculating the y coordinates of Y:

`Y_y + y = Y'_y`

This gives

`Y_y + 6 = 7`

`Y_y = 7 - 6`

`Y_y = 1`

Hence:

`Y(x,y) = (13,1)`