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2 years ago

Trapezoid W′X′Y′Z′ is the image of trapezoid WXYZ under a dilation through point C.

Mathematics

2 answers:

dem82 [27]2 years ago

8 0

Answer:

Option C.

Step-by-step explanation:

Given information: WX=8m and W'X'=6m

It is given that Trapezoid W′X′Y′Z′ is the image of trapezoid WXYZ under a dilation through point C.

Scale factor is the ratio of corresponding sides of image and preimage.

$\text{Scale factor}=\frac{Corresponding side of image}{Corresponding side of preimage}$

For the given figure,

$\text{Scale factor}=\frac{W'X'}{WX}$

$\text{Scale factor}=\frac{6}{8}$

$\text{Scale factor}=\frac{3}{4}$

Since image and preimage lie on the same side of the center of dilation. So, the scale factor is positive number.

Therefore, the correct option is C.

Luda [366]2 years ago

4 0

The answer is 3 over 4

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3 years ago

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Answer:

Step-by-step explanation:

As the statement is ‘‘if and only if’’ we need to prove two implications

$f : X \rightarrow Y$ is surjective implies there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ .
If there exists a function $h : Y \rightarrow X$ such that $f\circ h = 1_Y$ , then $f : X \rightarrow Y$ is surjective

Let us start by the first implication.

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From each set $X_y$ choose only one element $x_y$ , and notice that $f(x_y)=y$ .

So, we can define the function $h:Y\rightarrow X$ as $h(y)=x_y$ . It is no difficult to conclude that $f\circ h(y) = f(x_y)=y$ . With this we have that $f\circ h=1_Y$ , and the prove is complete.

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Trapezoid W′X′Y′Z′ ​ is the image of trapezoid WXYZ under a dilation through point C.

Trapezoid W′X′Y′Z′ is the image of trapezoid WXYZ under a dilation through point C.