Question

write the coordinates of the vertices after a translation 3 units left and 5 units down.

Explanation:

Step1: Find original coordinates

From the graph, the original vertices are: \( E(1, 4) \), \( F(8, 4) \), \( G(8, -3) \), \( D(1, -3) \).

Step2: Apply translation (left 3, down 5)

For a point \((x, y)\), translation 3 units left (subtract 3 from \(x\)) and 5 units down (subtract 5 from \(y\)) gives \((x - 3, y - 5)\).

• For \( E(1, 4) \): \( (1 - 3, 4 - 5) = (-2, -1) \)
• For \( F(8, 4) \): \( (8 - 3, 4 - 5) = (5, -1) \)
• For \( G(8, -3) \): \( (8 - 3, -3 - 5) = (5, -8) \)
• For \( D(1, -3) \): \( (1 - 3, -3 - 5) = (-2, -8) \)

Answer:

The new coordinates of the vertices are \( E'(-2, -1) \), \( F'(5, -1) \), \( G'(5, -8) \), \( D'(-2, -8) \).