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Question
Use the image to answer the question.
A solid-line quadrilateral has vertices upper A, upper B, upper C, and upper D. A dotted-line quadrilateral has vertices upper E, upper F, upper G, and upper H. The coordinates of the first quadrilateral are as follows: upper A at left parenthesis 2 comma 2 right parenthesis, upper B at left parenthesis 6 comma 4 right parenthesis, upper C at left parenthesis 10 comma 4 right parenthesis, and upper D at left parenthesis 6 comma 2 right parenthesis. The second quadrilateral has the following coordinates: upper E at left parenthesis 11 comma negative 1 right parenthesis, upper F at left parenthesis 15 comma negative 1 right parenthesis, upper G at left parenthesis 19 comma 1 right parenthesis, and upper H at left parenthesis 15 comma 1 right parenthesis.
Translate quadrilateral ABCD
by 2 units to the right and 4 units up. Which of the following are the coordinates of new quadrilateral A′B′C′D′
?
(1 point)
Responses
A′(7,7)
, B′(10,9)
, C′(12,7)
, D′(10,5)
cap A prime times open paren 7 comma 7 close paren, cap b prime times open paren 10 comma 9 close paren, cap c prime times open paren 12 comma 7 close paren, cap d prime times open paren 10 comma 5 close paren - no response given
A′(7,−1)
, B′(10,1)
, C′(12,−1)
, D′(10,−3)
cap A prime times open paren 7 comma negative 1 close paren, cap b prime times open paren 10 comma 1 close paren, cap c prime times open paren 12 comma negative 1 close paren, cap d prime times open paren 10 comma negative 3 close paren - no response given
A′(3,−1)
, B′(6,1)
, C′(8,−1)
, D′(6,−3)
cap A prime times open paren 3 comma negative 1 close paren, cap b prime times open paren 6 comma 1 close paren, cap c prime times open paren 8 comma negative 1 close paren, cap d prime times open paren 6 comma negative 3 close paren - no response given
A′(3,7)
, B′(6,9)
, C′(8,7)
, D′(6,5)
1 answer
To find the new coordinates \( A'B'C'D' \) of quadrilateral \( ABCD \) after translating it by 2 units to the right and 4 units up, we can apply the transformation to each vertex of the original quadrilateral.
The original coordinates of the quadrilateral \( ABCD \) are:
\( A(2, 2) \)
\( B(6, 4) \)
\( C(10, 4) \)
\( D(6, 2) \)
Translation:
Translating by 2 units to the right means adding 2 to the x-coordinates.
Translating by 4 units up means adding 4 to the y-coordinates.
Calculating the new coordinates:
For \( A(2, 2) \):
\[
A' = (2 + 2, 2 + 4) = (4, 6)
\]
For \( B(6, 4) \):
\[
B' = (6 + 2, 4 + 4) = (8, 8)
\]
For \( C(10, 4) \):
\[
C' = (10 + 2, 4 + 4) = (12, 8)
\]
For \( D(6, 2) \):
\[
D' = (6 + 2, 2 + 4) = (8, 6)
\]
Thus, the new coordinates for the quadrilateral \( A'B'C'D' \):
\( A'(4, 6) \)
\( B'(8, 8) \)
\( C'(12, 8) \)
\( D'(8, 6) \)
It appears that none of the given responses match the calculated coordinates of \( A'B'C'D' \). Please double-check the vertices provided for the original quadrilateral \( ABCD \) or the translation instructions.
