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dem82 [27]
3 years ago
10

If rectangle ABCD, defined by the coordinates A(0, 0), B(0, -4), C(-2, -4), D(-2, 0), is dilated by a scale factor of 2, with re

sulting vertex A' at (2, 4), what is the center of the dilation? A) (0, 0) Eliminate B) (2, 4) C) (0, -4) D) (-2, -4)
Mathematics
1 answer:
notsponge [240]3 years ago
6 0

Answer:

D) (-2, -4).

Step-by-step explanation:

Let (x, y) be the center of dilation. Imagine that (x, y) is the center of origin of a new Cartesian Plane. What would the coordinates of point A and A' on the new plane?

  • A: (0 - x, 0 - y) ⇒ (-x, -y).
  • A': (2 - x, 4 - y).

Dilating (-x, -y) about the "origin" of the new plane by a factor of two will give the point (-{\bf 2}x, -{\bf 2}y), also on the new plane.

For coordinates of A' on the original plane,

(-{2}x, -{2}y) = (2 - x, 4 - y).

As a result,

\left \{ \begin{array}{l}-2x = 2 - x\\-2 y = 4 - y\end{array}.

\left \{ \begin{array}{l}-x = 2\\- y = 4\end{array}.

\left \{ \begin{array}{l}x = -2\\y = -4\end{array}.

In other words, {\bf (-2, -4)} is the center of dilation.

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In the diagram, transversal t cuts parallel lines a and b. Which equation is necessarily true?
hoa [83]

Answer:

The correct answer is option B.  

m<3 = m<6

Step-by-step explanation:

From the figure we an see that, a and b are parallel lines and line t is the traversal on the lines.

<u>To find the correct option</u>

From the given figure we get

Corresponding angles are,

<1 & <5,  <2&<6, <2&<7 and <4 &<8

Alternate interior angles are,

<3 & <6  and <4 &<5

Alternate interior angles are equal.

m<3 = m<6

Therefore the correct answer is optionB

3 0
3 years ago
Read 2 more answers
Easyish PreCalculus; Find the exact values of the six trigonometric functions of the given angle. (you can use a calculator.) (D
Brut [27]

Answer:

there is no given angle here man

Step-by-step explanation:

5 0
3 years ago
ASAP!!! Please help!!!
Sunny_sXe [5.5K]

Answer:

-\frac{28}{99}

Step-by-step explanation:

To divide a fraction by a fraction, flip the second fraction and change the divide sign into a multiplication sign.

\frac{4}{9}\div -\left(\frac{11}{7}\right)=\frac{4}{9} *-\frac{7}{11}

Multiply:

-\frac{4*7}{9*11}

-\frac{28}{99}

6 0
3 years ago
Evaluate the expression <br> 3p – 2q + 6 when p = 8 and q = -2
Yuliya22 [10]

Answer:

34

Step-by-step explanation:

substitute

3(8)-2(-2)+6

dsitribute

24+4+6

add

34

3 0
3 years ago
1/4 the difference of 4/6 + 3/12
Soloha48 [4]
The answer would be about 8/12 because you must convert 4/6 into 8/12. 8/12 + 3/12=11/12 
1/4 would be about  3/12, so 11/12 - 3/12=8/12.
5 0
3 years ago
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