Question

Quadrilateral DEFG has vertices D(-1,2), E(-2, 0), F(-1,-1) and G(1, 3). A

translation maps quadrilateral DEFG to quadrilateral D'E'F'G'. The image of D is D'(-2,-2).
What are the coordinates of E, F, and G′ ?

Answer 1

E' = (-3, -4)

F' = (-2, -5)

G' = (0, -1)

Explanation:

Given vertices of quadrilateral DEFG:

• D = (-1, 2)
• E = (-2, 0)
• F = (-1, -1)
• G = (1, 3)

A translation is a type of transformation and moves a figure left, right, up or down.

Every point on the original figure is translated (moved) the same distance in the same direction.

Therefore, to calculate the mapping rule that translates DEFG to D'E'F'G', compare the coordinates of D with the coordinates of D'.

• D = (-1, 2)
• D' = (-2, -2)

The x-coordinate has be translated 1 unit to the left.

The y-coordinate has been translated 4 units down.

Therefore, the mapping rule is:

• (x, y) → (x-1, y-4)

To find the coordinates of E', F' and G', apply the mapping rule to the given vertices of the pre-image:

⇒ E' = (-2-1, 0-4) = (-3, -4)

⇒ F' = (-1-1, -1-4) = (-2, -5)

⇒ G' = (1-1, 3-4) = (0, -1)