Given the coordinates of recatangle ABCD:
A(-3, 1), B(2, 1), C(2, -2), D(-3, -2)
Let's find the new coordinates after the rectangle is translated 4 units horizontally and -2 units vertically.
Let's apply rules of translation.
A translation 4 units horizontally means a shift 4 units to the right.
It is written as: (x + 4)
A translation -2 units vertically means a shift 2 units downwards.
It is written as: (y - 2)
Thus, to find the new coordinates, add 4 to the x-coordinates and subtract 2 from the y-cooridnates.
We have the translation rule: (x + 4, y - 2)
We have:
A(-3, 1) ==> (-3 + 4, 1 - 2) ==> A'(1, -1)
B(2, 1) ==> (2 + 4, 1 - 2) ==> B'(6, -1)
C(2, -2) ==> (2 + 4, -2 - 2) ==> C'(6, -4)
D(-3, -2) ==> (-3 + 4, -2 - 2) ==> (1, -4)
Therefore, the new coordintes of the figure are:
A'(1, -1), B'(6, -1), C'(6, -4), D(1, -4)
ANSWER:
A'(1, -1), B'(6, -1), C'(6, -4), D'(1, -4)