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Aliun [14]
3 years ago
15

Two similar triangles are shown on the coordinate grid:

Mathematics
1 answer:
Andreas93 [3]3 years ago
8 0

Answer:

The set of transformations has been performed on triangle ABC is dilation by a scale factor of 2 followed by reflection about the x-axis

Step-by-step explanation:

Let us write the vertices of Δ ABC

∵ Vertex A = (-2, -1)

∵ Vertex B = (0, 0)

∵ Vertex C = (1, -3)

Let us Write the vertices of Δ A'B'C'

∵ Vertex A' = (-4, 2)

∵ Vertex B' = (0, 0)

∵ Vertex C' = (2, 6)

Let us find the scale factor k between the x-coordinates of the points and their images.

∵ -4 = k (-2) ⇒ Divide both side by -2

∵ \frac{-4}{-2} = \frac{-2k}{-2}

∴ 2 = k

∴ The scale factor of a dilation is 2

∵ The signs of the y-coordinates of the images are the opposite of

    the signs of the y-coordinates of the points

∴ The triangle is reflected about the x-axis

∴ The set of transformations has been performed on triangle ABC

   is dilation by a scale factor of 2 followed by reflection about the x-axis

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Read 2 more answers
If m<ECD is six less than five times m<BCE. and m<BCD = 162°, find each measure.(Sorry bout using the wrong signs, but
tia_tia [17]

Answer:

m∠BCE = 28° and m∠ECD = 134°

Step-by-step explanation:

* Lets explain how to solve the problem

- The figure has three angles: ∠BCE , ∠ECD , and ∠BCD

- m∠ECD is six less than five times m∠BCE

- That means when we multiply measure of angle BCE by five and

 then subtract six from this product the answer will be the measure

 of angle ECD

∴ m∠ECD = 5 m∠BCE - 6 ⇒ (1)

∵ m∠BCD = m∠BCE + m∠ECD

∵ m∠BCD = 162°

∴ m∠BCE + m∠ECD = 162 ⇒ (2)

- Substitute equation (1) in equation (2) to replace angle ECD by

  angle BCE

∴ m∠BCE + (5 m∠BCE - 6) = 162

- Add the like terms

∴ 6 m∠BCE - 6 = 162

- Add 6 to both sides

∴ 6 m∠BCE = 168

- Divide both sides by 6

∴ m∠BCE = 28°

- Substitute the measure of angle BCE in equation (1) to find the

  measure of angle ECD

∵ m∠ECD = 5 m∠BCE - 6

∵ m∠BCE = 28°

∴ m∠ECD = 5(28) - 6 = 140 - 6 = 134°

* m∠BCE = 28° and m∠ECD = 134°

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3 years ago
Read 2 more answers
The number of students at jefferson school is even. The number has three digits. The digit in the ten place is 4. write there nu
Burka [1]
Let's assign three blanks for each digit of the unknown number. But let's fill in the tens digit because it is already specified.

_ 4 _

The last digit should be even to make it even. The possible digits for this are 2, 4, 6, and 8. The first digit could be any digit from 1 to 9. Therefore, the possible answers are 

142  242  342  442  542  642  742  842  942
144  244  344  444  544  644  744  844  944
146  246  346  446  546  646  746  846  946
148  248  348  448  548  648  748  848  948

Therefore, there are a total of 36 possible answers.

5 0
3 years ago
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