Question

graph the image of rectangle cdef after a translation 4 units left and 9 units up.

Explanation:

Step1: Find coordinates of CDEF

First, identify the coordinates of the vertices of rectangle \( CDEF \):

• \( F(-6, 0) \)
• \( E(-2, 0) \)
• \( D(-2, -6) \)
• \( C(-6, -6) \)

Step2: Apply translation (left 4, up 9)

A translation 4 units left means subtract 4 from the \( x \)-coordinate, and 9 units up means add 9 to the \( y \)-coordinate. The translation rule is \( (x, y) \to (x - 4, y + 9) \).

• For \( F(-6, 0) \):

New \( x \): \( -6 - 4 = -10 \), New \( y \): \( 0 + 9 = 9 \). So \( F'(-10, 9) \).

• For \( E(-2, 0) \):

New \( x \): \( -2 - 4 = -6 \), New \( y \): \( 0 + 9 = 9 \). So \( E'(-6, 9) \).

• For \( D(-2, -6) \):

New \( x \): \( -2 - 4 = -6 \), New \( y \): \( -6 + 9 = 3 \). So \( D'(-6, 3) \).

• For \( C(-6, -6) \):

New \( x \): \( -6 - 4 = -10 \), New \( y \): \( -6 + 9 = 3 \). So \( C'(-10, 3) \).

Step3: Plot the new points

Plot \( F'(-10, 9) \), \( E'(-6, 9) \), \( D'(-6, 3) \), and \( C'(-10, 3) \), then connect them to form the translated rectangle.

Answer:

The translated rectangle has vertices at \( \boldsymbol{F'(-10, 9)} \), \( \boldsymbol{E'(-6, 9)} \), \( \boldsymbol{D'(-6, 3)} \), and \( \boldsymbol{C'(-10, 3)} \). (Graph by plotting these points and connecting them.)