Quadrilateral ABCD is graphed on a coordinate plane with the vertices A(-9,6), 3(-4,-6), C(-3,2), and D(-3,-2)
A. Quadrilateral ABCD is translated to the left 2 units and up 6 units. Write the translation in terms of x and y using
ordered pair notation
B. Determine the coordinates of the vertices of the image. Be sure to name each of the vertices of the image with the
correct notation

If the point (x , y) translated horizontally to the right by h units then its image is (x + h , y)
If the point (x , y) translated horizontally to the left by h units then its image is (x - h , y)
If the point (x , y) translated vertically up by k units then its image is (x , y + k)
If the point (x , y) translated vertically down by k units then its image is (x , y - k)

A.

∵ Quadrilateral ABCD is translated to the left 2 units and up 6 units

- That means subtract 2 from each x-coordinates and add 6

to each y-coordinates

∵ (x , y) is moved to the left 2 units ad up 6 units

∴ Its image is (x - 2 , y + 6)

The translation rule is (x , y) → (x - 2 , y + 6)

B.

∵ The vertices of the quadrilateral ABCD are

A (-9 , 6) , B (-4 , -6) , C (-3 , 2) , D (-3 , -2)

∵ Quadrilateral ABCD is translated to the left 2 units and up 6 units

- Use the rule in part A to find the image of each vertex

∵ A' = (-9 - 2 , 6 + 6)

∴ A' = (-11 , 12)

∵ B' = (-4 - 2 , -6 + 6)

∴ B' = (-6 , 0)

∵ C' = (-3 - 2 , 2 + 6)

∴ C' = (-5 , 8)

∵ D' = (-3 - 2 , -2 + 6)

∴ D' = (-5 , 4)

The coordinates of the vertices of the image are A' (-11 , 12) , B' (-6 , 0) , C' (-5 , 8) , D' (-5 , 4)

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