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Burka [1]
3 years ago
12

A 2x2 square is centered on the origin. It is dilated by a factor of 3. What are the coordinated of the vertices of the square?

What is the ratio of the areas from the larger square to the smaller square?
Mathematics
1 answer:
Alexxx [7]3 years ago
5 0

<u>Answer</u>:

The vertices are:

A' = (-3, -3)

B' = (3, -3)

C' = (3, 3)

D' = (-3, 3)

The ratio of area of  larger square to smaller square is 9:1

<u>Step-by-step explanation:</u>

Given:

A 2 x 2 square is centered at the origin.

So, the center of the square is (0, 0)

Since it is 2 x 2 square, the side of the square is 2 units.

So, the vertices of the 2 x 2 square are A (-1, -1),  B(1, -1), C(1. 1), D(-1, 1)

The above square is dilated by a factor of 3.

Let's name the dilated square A'B'C'D'

To find the coordinates of the vertices of dilated square, we need to multiply each vertices of ABCD by 3.

A(-1, -1) = 3(-1, -1) = A'(-3, -3)

B(1, -1) = 3(1, -1) = B'(3, -3)

C(1, 1) = 3(1, 1) = C'(3, 3)

D(-1, 1) = 3(-1, 1) = D'(-3, 3)

To find the area of the small square

the side  of the small square is 2 units

so the are of the small square is 2^2 = 4 square units

To find the area of the larger square

lets find the side AB of the square using distance formula

=>\sqrt{(x_2 -x_1)^2 +(y_2-y_1)^2}

=>\sqrt{(3 - (-3))^2 +(-3 - (-3))^2}

=>\sqrt{(3 +3)^2 +(-3 +3)^2}

=>\sqrt{(6)^2 +(0)^2}

=>\sqrt{36}

=>6

AB =6 units

In a square all the sides will be equal

Now the area of the larger square will be

6^2

36 square units

The ratio of larger square to smaller square is

=>36 : 4

=>9 : 1

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Answer:

1. (x +1)(x - 1)

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Step-by-step explanation:

The first 4 expressions can be factored with the difference of squares type of factoring.

For #5, the odd one out is (x+5)(x-7) because it isn't a factor of any of the standard form equations, while the others are

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3 years ago
The Louvre is an art museum in Paris. A glass square base pyramid sits in front of the entrance to the museum. If the pyramid is
Sveta_85 [38]

Answer:

lateral area = 2320 m²

Step-by-step explanation:

The question wants us to calculate the lateral area of a square base pyramid. The square base pyramid has a side of 40 meters.The height is 21 meters.

Half of the square base is 40/2 =  20 meters . With the height it forms a right angle triangle. The hypotenuse side is the slant height of the pyramid.

Using Pythagoras's theorem

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c² = 400 + 441

c² = 841

square root both sides

c = √841

c = 29 meters

The slant height of the pyramid is 29 meters.

The pyramid has four sided triangle. The lateral area is 4 multiply by the area of one triangle.

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area = 580

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3 years ago
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3 years ago
(4x + 3)(4x - 3)<br> Help pls
tekilochka [14]

Answer:

16x^2-9

Step-by-step explanation:

\left(4x+3\right)\left(4x-3\right)

We´ll <u>Apply Difference Two Squares Formula:</u>

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\longmapsto \left(4x+3\right)\left(4x-3\right)

\longmapsto \left(4x\right)^2-3^2

<u>Apply exponent rule</u>:

  • \left(a\times \:b\right)^n=a^nb^n

\longmapsto 4^2x^2-3^2

\longmapsto 16x^2-9

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