Question

write the coordinates of the vertices after a translation 8 units down.
b(
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c(
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d(
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e(
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Explanation:

Step1: Find original coordinates

First, identify the original coordinates of each vertex from the graph.

• \( B(-7, 5) \) (since it's 7 units left on x - axis and 5 units up on y - axis)
• \( C(3, 5) \) (3 units right on x - axis and 5 units up on y - axis)
• \( D(3, 7) \) (3 units right on x - axis and 7 units up on y - axis)
• \( E(-7, 7) \) (7 units left on x - axis and 7 units up on y - axis)

Step2: Apply translation (8 units down)

A translation 8 units down means we subtract 8 from the y - coordinate of each vertex. The rule for a translation 8 units down is \((x,y)\to(x,y - 8)\)

• For \( B(-7,5) \):

New \( x=-7 \), new \( y = 5-8=-3 \), so \( B'(-7,-3) \)

• For \( C(3,5) \):

New \( x = 3 \), new \( y=5 - 8=-3 \), so \( C'(3,-3) \)

• For \( D(3,7) \):

New \( x = 3 \), new \( y=7 - 8=-1 \), so \( D'(3,-1) \)

• For \( E(-7,7) \):

New \( x=-7 \), new \( y=7 - 8=-1 \), so \( E'(-7,-1) \)

Answer:

\( B'(-7, - 3) \)
\( C'(3, - 3) \)
\( D'(3, - 1) \)
\( E'(-7, - 1) \)