Question

Quadrilateral ABCD has vertices A (-1,8), B (2, 12), C (5,8), and D (-1,-2)

and its image has a translation (x, y) - (x + 12, y-5). What are the new
coordinates of A'B'C'D'?​

Answer 1

The new coordinates of A'B'C'D' are
`A'(x,y) =(11,3)`,
`B'(x,y) = (14, 7)`,
`C'(x,y) = (17, 3)` and
`D'(x,y) = (11, -7)`, respectively.

Explanation:

By using the translation definition, we get the coordinates of the quadrilateral A'B'C'D':

`A'(x,y) = A(x,y) + T(x,y)` (1)

`A'(x,y) = (-1,8) + (12,-5)`

`A'(x,y) =(11,3)`

`B'(x,y) = B(x,y) + T(x,y)` (2)

`B'(x,y) = (2,12) + (12,-5)`

`B'(x,y) = (14, 7)`

`C'(x,y) = C(x,y) + T(x,y)` (3)

`C'(x,y) = (5,8) + (12,-5)`

`C'(x,y) = (17, 3)`

`D'(x,y) = D(x,y) +T(x,y)` (4)

`D'(x,y) = (-1,-2) + (12,-5)`

`D'(x,y) = (11, -7)`

The new coordinates of A'B'C'D' are
`A'(x,y) =(11,3)`,
`B'(x,y) = (14, 7)`,
`C'(x,y) = (17, 3)` and
`D'(x,y) = (11, -7)`, respectively.