Question

A sequence of translations maps a GHI to AG'H'T.

• AGHI has vertices at G (-8, 2), H (13,2), and (-2, 10). .

• The coordinates of G'are (-1,-3).

What are the coordinates for ' and '?

H=
I=

Answer 1

Since we know that AGHI maps to AG'H'T, we can assume that the translation maps each corresponding vertex to its prime (') counterpart. Therefore, the coordinates of H' and I' can be found by applying the same translation that takes G to G'.

To find the translation vector, we can subtract the coordinates of G from the coordinates of G':

Translation vector = G' - G

= (-1, -3) - (-8, 2)

= (-1 + 8, -3 - 2)

= (7, -5)

Now, we can use this translation vector to find H' and I':

H' = H + Translation vector

= (13, 2) + (7, -5)

= (13 + 7, 2 - 5)

= (20, -3)

I' = (-2, 10) + (7, -5)

= (-2 + 7, 10 - 5)

= (5, 5)

Therefore, the coordinates for H' are (20, -3) and for I' are (5, 5).