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IRISSAK [1]
3 years ago
8

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 t

he transformation that shows it is congruent to ABCD. E(-3, -4), F(1, -3), G(3, -6), and H(1, -6) a translation 7 units right E(-3, -1), F(1, -2), G(3, 1), and H(1, 1) 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(4, 4), F(8, 3), G(10, 6), and H(8, 6) a translation 5 units down
Mathematics
1 answer:
kykrilka [37]3 years ago
7 0

Answer:

1) E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)   a reflection across the x-axis

2) E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)       a translation 5 units down

3) E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)    a reflection across the y-axis

4) E(4, 4), F(8, 3), G(10, 6), and H(8, 6)    a translation 7 units right

Step-by-step explanation:

Quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6).

1) E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

In this case the vertices has the same abscissas, and the ordinates have opposite sign, then the transformation is a reflection across the x-axis.


2) E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

In this case the vertices has the same abscissas, and the ordinates of EFGH have 5 units less, then the transformation is a translation 5 units down.


3) E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

In this case the vertices has the same ordinates, and the abcissas have opposite sign, then the transformation is a reflection across the y-axis.


4) E(4, 4), F(8, 3), G(10, 6), and H(8, 6)

   A(-3, 4), B(1, 3), C(3, 6), and D(1, 6)

In this case the vertices has the same ordinates, and the abscissas of EFGH have 7 units more, then the transformation is a translation 7 units right.

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Step-by-step explanation:

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mamaluj [8]

We know that the perimeter of a rectangle is twice the length, plus twice the width.  

P = 2L + 2W  

We also know that the perimeter is 156.  

P = 156  

Finally, we know that the width is 12 less than the length.  

W = L - 12.  

The next thing that we do is substitute the information that we have into the original equation:  

P = 2L + 2W  

156 = 2L + 2(L - 12)  

From this point we start to solve  

156 = 2L + 2L - 24 <---we multiplied the '2' through the parenthesis  

156 + 24 = 2L + 2L - 24 + 24  

180 = 2L + 2L <--- getting like terms on same sides  

180 = 4L <---combining like terms  

180/4 = 4L/4 <--- getting like terms on same sides  

45 = L <---now we have a value for L  

Now we take the known value for L and substitute it in to our equation for W  

W = L - 12  

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W = 33  

So now we have Length = 45 and Width = 33.

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3 years ago
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