Answer:
Correct Pairs:
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:
In Mathematics Geometry, translation just means 'moving'. A move without altering the size, rotation or anything else. When you perform a translation on a shape, the coordinates of that shape will change.
Translation right means you would add the translated unit to the x-coordinates of the of the point, let say P(x, y), in the original object.
Translation down means you would subtract the translated unit from the y-coordinates of the of the point, let say P(x, y), in the original object.
In Mathematics, a reflection just means a 'flip' over a line.
A reflection across x axis means, if a point P(x, y) is reflected across the x-axis, the x coordinate remains the same, while y coordinate changes its sign. i.e. the point (x, y) is changed to (x, -y).
A reflection across y axis means, if a point P(x, y) is reflected across the y-axis, the y coordinate remains the same, while x coordinate changes its sign. i.e. the point (x, y) is changed to (-x, y).
Now, lets head towards the solution:
Analyzing "a translation 7 units right"
As the given ABCD Quadrilateral has vertices as A (-3, 4), B (1, 3), C (3, 6) and D (1, 6).
As EFGH is congruent to ABCD.
And
A translation of ABCD 7 units right would bring the following transformation:
A (-3, 4), B (1, 3), C (3, 6) and D(1, 6) ⇒ A'(4, 4), B'(8, 3), C'(10, 6), and D'(8, 6)
As EFGH ≅ ABCD
So,
Here are the matching vertices when a translation 7 units right is made:
E(4, 4), F(8, 3), G(10, 6), and H(8, 6) ⇒ a translation 7 units right
Analyzing "a reflection across the y-axis"
As the given ABCD Quadrilateral has vertices as A (-3, 4), B (1, 3), C (3, 6) and D (1, 6).
As EFGH is congruent to ABCD.
And
A reflection of ABCD across the y-axis would bring the following transformation:
A(-3, 4), B (1, 3), C(3, 6) and D(1, 6) ⇒ A' (3, 4), B'(-1, 3), C'(-3, 6) and D'(-1, 6)
As EFGH ≅ ABCD
So,
Here are the matching vertices when a reflection across the y-axis is made:
E(3,4), F(-1,3), G(-3, 6), and H(-1,6) ⇒ a reflection across the y-axis
Analyzing "a reflection across the x-axis"
As the given ABCD Quadrilateral has vertices as A (-3, 4), B (1, 3), C (3, 6) and D (1, 6).
As EFGH is congruent to ABCD.
And
A reflection of ABCD across the x-axis would bring the following transformation:
A(-3, 4), B (1, 3), C(3, 6) and D(1, 6) ⇒ A' (-3, -4), B'(1, -3), C'(3, -6) and D'(1, -6)
As EFGH ≅ ABCD
So,
Here are the matching vertices when a reflection across the x-axis is made:
E(-3,-4), F(1,-3), G(3,-6), and H(1,-6) ⇒ a reflection across the x-axis
Analyzing "a translation 5 units down"
As the given ABCD Quadrilateral has vertices as A (-3, 4), B (1, 3), C (3, 6) and D (1, 6).
As EFGH is congruent to ABCD.
And
A translation of ABCD 5 units down brings the following transformation:
A (-3, 4), B (1, 3), C (3, 6) and D(1, 6) ⇒ A' (-3, -1), B'(1, -2), C'(3, 1) and D'(1, 1)
As EFGH ≅ ABCD
So,
Here are the matching vertices when a translation 5 units down is made:
E(-3,-1), F(1,-2), G(3, 1), and H(1,1) ⇒ a translation 5 units down
Here is summary of matched Pairs:
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
Keywords: reflection, translation, transformation
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