Question

Quadrilateral KLMN has vertices K(-2,-2), L(1,1), M(0,4), and N(-3,5). It is first translated by (x + 2,y - 1) and then translated by (x - 3,y + 4). When a figure is translated twice, a double prime symbol is used. Find the coordinates of K" L" M" N" after both translations.

Answer 1

K''(-3;1)

L''(0;4)

M''(-1;7)

N''(-4;8)

Explanation:

To find the first Translation, K'L'M'N', 2 must be added to each x-coordinate and 1 subtracted from each y-coordinate of the original points:

K'(0;-3)

L'(3;0)

M'(2;3)

N'(-1;4)

To find the second translation, K''L''M''N'', 3 must be subtracted from each x-coordinate and add 4 to each y-coordinate of the new translated points:

K''(-3;1)

L''(0;4)

M''(-1;7)

N''(-4;8)

Answer 2

Quadrilateral KLMN has vertices K(-2,-2), L(1,1), M(0,4), and N(-3,5)
It is first translated by (x + 2,y - 1)
then
K(-2,-2) ---> K'(-2 + 2,-2 - 1) = (0,-3)
L(1,1), ---> L'(1 + 2,1 - 1) = (3,0)
M(0,4), ---> M' (0 + 2,4 - 1) = (2,3)
and
N(-3,5) ---> N' (-3 + 2,5 - 1) = (-1,4)
and then translated by (x - 3,y + 4)
K'(0,-3) ---> K''(0 - 3,-3 + 4) = (-3,1)
L'(3,0) ---> L''(3 - 3,0 + 4)= (0,4)
M'(2,3) ---> M'' (2 - 3, 3 + 4)= (-1,7)
and
N'(-1,4) ---> N'' (-1 - 3,4 + 4) = (-4,8)
the coordinates of K" L" M" N" after both translations are
K''= (-3,1)
L''= (0,4)
M''= (-1,7)
and
N'' = (-4,8)