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3 years ago

Need urgent help!?

2 answers:

5 0

Writing both in slope intercept form:
Line 1:
2x + 2y = 4 Subtract 2x
2y = -2x + 4 Divide both sides by 2
y = -x + 2

Line 2:
y = -x + 5

The lines have the same slope, -1, and different y-intercepts.

They are parallel lines

zheka24 [161]3 years ago

4 0

Look at the slope:
2x+2y=4 =>2y=-2x+4 =>y=-x+2 the slope is -1, the same as the line y=-x+5, so the two lines are parallel.

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Question:

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part A) The scale factor of the sides (small to large) is 1/2

part B) Te ratio of the areas (small to large) is 1/4

part C) see the explanation

Step-by-step explanation:

Part A) Determine the scale factor of the sides (small to large).

we know that

The dilation is a non rigid transformation that produce similar figures

If two figures are similar, then the ratio of its corresponding sides is proportional

Let

z ----> the scale factor

$\frac{CB}{C'B'}=\frac{CD}{C'D'}=\frac{BD}{B'D'}$

The scale factor is equal to

$z=\frac{CB}{C'B'}$

substitute

$z=\frac{4}{8}$

simplify

$z=\frac{1}{2}$

Part B) What is the ratio of the areas (small to large)?

Area of the small triangle

$A=\frac{1}{2}(2)(4)=4\ units^2$

Area of the large triangle

$A=\frac{1}{2}(4)(8)=16\ units^2$

ratio of the areas (small to large)

$ratio=\frac{4}{16}=\frac{1}{4}$

Part C) Write a generalization about the ratio of the sides and the ratio of the areas of similar figures

In similar figures the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In similar figures the ratio of its areas is equal to the scale factor squared

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