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3 years ago

Line segment AB was dilated to create line segment A'B' using the dilation rule DQ,0.15.

Mathematics

1 answer:

krok68 [10]3 years ago

8 0

Answer:

13.6

Step-by-step explanation:

The measure of the segment AQ is related to the measure of the segment A'Q by the dilation factor as follows:

dilation factor = A'Q/AQ

AQ = A'Q/dilation factor

Replacing with data:

AQ = 2.4/0.15 = 16

Then, the distance between points A and A' is

x = 16 - 2.4 = 13.6

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3 years ago

Which of the following statements is true if m∠E = m∠Y and m∠F = m∠X?

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Answer:

segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If m∠E = m∠Y and m∠F = m∠X

then

Triangles EFG and YXZ are similar by AA Similarity Theorem

Remember that

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

In this problem

The corresponding sides are

FE and XY

EG and YZ

GF and ZX

so therefore

segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX Firstly , let us learn about trigonometry in mathematics.

Suppose the ΔABC is a right triangle and ∠A is 90°.

sin ∠A = opposite / hypotenuse

cos ∠A = adjacent / hypotenuse

tan ∠A = opposite / adjacent

Let us now tackle the problem!

A similar triangle has the same angle, in other words the triangle has the same shape but different sizes.

From the figure in the attachment , we can conclude that:

m∠E = m∠Y

m∠F= m∠X

m∠G = m∠Z

∴ ΔEFG ~ ΔYXZ ( ΔEFG is similar to ΔYXZ )

Because of the similarity , then:

FE : XY = EG : YZ = GF : ZX

Conclusion:

ΔFG is similar to ΔYXZ.

Segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX , i.e:

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle

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