Question

write the coordinates of the vertices after a translation 4 units right and 1 unit up.

Explanation:

First, we need to determine the original coordinates of the vertices \( C \), \( D \), and \( E \) from the graph.

Step 1: Find original coordinates

• For point \( D \): Looking at the graph, the x - coordinate is - 6 and the y - coordinate is - 3. So \( D(-6,-3) \)
• For point \( C \): The x - coordinate is - 6 and the y - coordinate is - 9. So \( C(-6,-9) \)
• For point \( E \): The x - coordinate is - 2 and the y - coordinate is - 7. So \( E(-2,-7) \)

Step 2: Apply translation (4 units right, 1 unit up)

The rule for translation 4 units right (add 4 to the x - coordinate) and 1 unit up (add 1 to the y - coordinate) is \((x,y)\to(x + 4,y + 1)\)

• For point \( D(-6,-3)\):

New x - coordinate: \(-6+4=-2\)
New y - coordinate: \(-3 + 1=-2\)
So \( D'(-2,-2) \)

• For point \( C(-6,-9)\):

New x - coordinate: \(-6+4=-2\)
New y - coordinate: \(-9 + 1=-8\)
So \( C'(-2,-8) \)

• For point \( E(-2,-7)\):

New x - coordinate: \(-2+4 = 2\)
New y - coordinate: \(-7+1=-6\)
So \( E'(2,-6) \)

Answer:

The coordinates of the vertices after translation are \( D'(-2,-2) \), \( C'(-2,-8) \), \( E'(2,-6) \)