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Question

Parallelogram upper E upper F upper G upper H is graphed on a coordinate plane. The x-axis ranges from negative 8 to 8 in increments of 1. The y-axis ranges from negative 8 to 8 in increments of 1.
E=(-1, 5)
F=(2, 8)
G=(4, 4)
H=(1, 1)
Suppose the parallelogram on the coordinate plane is dilated in reference to the origin using a magnitude of 3. What would be the coordinates of the new vertices of E′F′G′H′ ?

(1 point)
Responses

E′(−3,15), F′(6,24), G′(12,12) and H′(3,3)
upper E prime left parenthesis negative 3 comma 15 right parenthesis , upper F prime left parenthesis 6 comma 24 right parenthesis , upper G prime left parenthesis 12 comma negative 12 right parenthesis and upper H prime left parenthesis 3 comma 3 right parenthesis

E′(2,8), F′(5,11), G′(7,7) and H′(4,4)
upper E prime left parenthesis 2 comma 18 right parenthesis , upper F prime left parenthesis 5 comma 11 right parenthesis , upper G prime left parenthesis 7 comma 7 right parenthesis and upper H prime left parenthesis 4 comma 4 right parenthesis

E′(−13,53), F′(23,83), G′(43,43) and H′(13,13)
upper E prime left parenthesis negative Start Fraction 1 over 3 End Fraction comma Start Fraction 5 over 3 End Fraction right parenthesis , upper F prime left parenthesis Start Fraction 2 over 3 End Fraction comma Start Fraction 8 over 3 End Fraction right parenthesis , upper G prime left parenthesis Start Fraction 4 over 3 End Fraction comma Start Fraction 4 over 3 End Fraction right parenthesis and upper H prime left parenthesis Start Fraction 1 over 3 End Fraction comma Start Fraction 1 over 3 End Fraction right parenthesis

E′(−4,2), F′(−1,5), G′(1,1) and H′(−2,−2)

Answer 1

To find the coordinates of the new vertices \(E', F', G', H'\) after a dilation centered at the origin with a scale factor of 3, you need to multiply the coordinates of each vertex of the parallelogram by 3.

The original coordinates are:

• \(E(-1, 5)\)
• \(F(2, 8)\)
• \(G(4, 4)\)
• \(H(1, 1)\)

Now, we'll apply the dilation:

1. For \(E' = (3 \times -1, 3 \times 5)\):

   • \(E' = (-3, 15)\)

2. For \(F' = (3 \times 2, 3 \times 8)\):

   • \(F' = (6, 24)\)

3. For \(G' = (3 \times 4, 3 \times 4)\):

   • \(G' = (12, 12)\)

4. For \(H' = (3 \times 1, 3 \times 1)\):

   • \(H' = (3, 3)\)

So, the new vertices after dilation are:

• \(E'(-3, 15)\)
• \(F'(6, 24)\)
• \(G'(12, 12)\)
• \(H'(3, 3)\)

Thus, the correct response is: \(E'(-3, 15), F'(6, 24), G'(12, 12) \text{ and } H'(3, 3)\).