Q:

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.

Accepted Solution

A:
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)