Question

Square GYTD has vertices G(−4,3) , Y(0, 3) , T(0,−1) and D(−4,−1) . ​ Square GYTD ​ is translated 2 units left and 2 units up to produce square G'Y'T'D' . Which coordinates describe the vertices of the image?
G'(−6, 5), Y'(−2, 5), T'(−2, 1) , and D′(−6, 1)
G'(−2, 5), Y'(2, 5), T'(2, 1) , and D′(−2, 1)
G'(−2, 1), Y'(2, 1), T'(2, −3) , and D′(−2, −3)
G'(−6, 1), Y'(−2, 1), T'(−2, −3) , and D′(−6, −3)

Answer 1

we know that

If square GYTD ​ is translated $2$ units left and  $2$ units up to produce square G'Y'T'D'

that means

the rule of transformation is

$(x,y)-------> (x-2,y+2)$

Find the coordinates of the image

$G (-4,3)------->G'(-4-2,3+2)=G'(-6,5)$

$Y (0,3)------->Y'(0-2,3+2)=Y'(-2,5)$

$T (0,-1)------->T'(0-2,-1+2)=T'(-2,1)$

$D (-4,-1)------->D'(-4-2,-1+2)=D'(-6,1)$

therefore

the answer is the option

G'(−6, 5), Y'(−2, 5), T'(−2, 1) , and D′(−6, 1)

Answer 2

The coordinates of the image are G'(-4 - 2, 3 + 2), Y'(0 - 2, 3 + 2), T'(0 - 2, -1 + 2), D'(-4 - 2, -1 + 2) = G'(-6, 5), Y'(-2, 5), T'(-2, 1), D'(-6, 1)