Quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6). Match each set of vertices of quadrilateral EFGH with the transformation that shows it is congruent to ABCD.
Answers
Explanation:
The correct match is
E(4, 4), F(8, 3), G(10, 6), and H(8, 6) a translation 7 units right
E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6) a reflection across the y-axis
E(-3, -4), F(1, -3), G(3, -6) and H(1, -6) a reflection across the x-axis
E(-3, -1), F(1, -2), G(3, 1), and H(1, 1) a translation 5 units down
Step-by-step explanation: Given that quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6).
We are given to match each of the given sets of quadrilateral EFGH with the transformation that shows it is congruent to ABCD.
Set A : A translation of 7 units right.
Under this translation, the co-ordinates of a point (x, y) changes to (x+7, y).
So, the vertices of quadrilateral ABCD changes as follows :
A(-3, 4) ⇒ (-3+7, 4) = (4, 4),
B(1, 3) ⇒ (1+7, 3) = (8, 3),
C(3, 6) ⇒ (3+7, 6) = (10, 6)
and
D(1, 6) ⇒ (1+7, 6) = (8, 6).
So, the co-ordinates of quadrilateral EFGH will be E(4, 4), F(8, 3), G(10, 6), and H(8, 6).
Set B : A reflection across the Y-axis.
Under this translation, the co-ordinates of a point (x, y) changes to (-x, y).
So, the vertices of quadrilateral ABCD changes as follows :
A(-3, 4) ⇒ (3, 4),
B(1, 3) ⇒ (-1, 3),
C(3, 6) ⇒ (-3, 6)
and
D(1, 6) ⇒ (-1, 6).
So, the co-ordinates of quadrilateral EFGH will be E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6).
Set C : A reflection across the X-axis.
Under this translation, the co-ordinates of a point (x, y) changes to (x, -y).
So, the vertices of quadrilateral ABCD changes as follows :
A(-3, 4) ⇒ (-3, -4),
B(1, 3) ⇒ (1, -3),
C(3, 6) ⇒ (3, -6)
and
D(1, 6) ⇒ (1, -6).
So, the co-ordinates of quadrilateral EFGH will be E(-3, -4), F(1, -3), G(3, -6) and H(1, -6).
Set D : A translation 5 units down..
Under this translation, the co-ordinates of a point (x, y) changes to (x, y-5).
So, the vertices of quadrilateral ABCD changes as follows :
A(-3, 4) ⇒ (-3, 4-5) = (-3, -1),
B(1, 3) ⇒ (1, 3-5) = (1, -2),
C(3, 6) ⇒ (3, 6-5) = (3, 1)
and
D(1, 6) ⇒ (1, 6-5) = (1, 1).
So, the co-ordinates of quadrilateral EFGH will be E(-3, -1), F(1, -2), G(3, 1), and H(1, 1).
Thus, the correct match is
E(4, 4), F(8, 3), G(10, 6), and H(8, 6) a translation 7 units right
E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6) a reflection across the y-axis
E(-3, -4), F(1, -3), G(3, -6) and H(1, -6) a reflection across the x-axis
E(-3, -1), F(1, -2), G(3, 1), and H(1, 1) a translation 5 units down.
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