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N76 [4]
3 years ago
14

Parallelogram FGHI on the coordinate plane below represents the drawing of a horse trail through a local park:

Mathematics
1 answer:
Masteriza [31]3 years ago
8 0

Answer:

The correct option is D.

Step-by-step explanation:

From the given figure it is noticed that the vertices of the parallelogram are F(-6,-1), G(-1,-1), H(-2,-4) and I(-7,-4).

In order to build a scale model of the trail, the drawing is enlarged on the coordinate plane.

Distance formula

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

FI=\sqrt{(-7-(-6))^2+(-4-(-1))^2}=\sqrt{1+9}=\sqrt{10}

AD=\sqrt{(1-3)^2+(2-8)^2}=\sqrt{4+36}=2\sqrt{10}

The scale factor is

\frac{AD}{FI}=\frac{2\sqrt{10}}{\sqrt{10}}=2

Therefore the length of sides of image is twice of preimage.

The vertices A and D are image of F and I respectively.

The length of FG is

FG=\sqrt{(-1-(-6))^2+(-1-(-1))^2}=\sqrt{25}=5

Therefore the length of AB is 10 units and length of CD is also 10 units.

The point which is on horizontal distance of 10 units from A(3,8), is B(13,8).

The point which is on horizontal distance of 10 units from D(1,2), is C(11,2).

Therefore vertices B and C are image of G and H respectively. The another corner points are (13,8) and (11,2). Option D is correct.

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Kenny buys 4 1liter bottles of water how many millileters of water does Kenny buy
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6 0
3 years ago
Which postulate or theorem can be used to
sveticcg [70]

Answer:

AA Similarity Postulate

Step-by-step explanation:

we know that

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

step 1

Verify the proportion of the corresponding sides

\frac{PS}{PQ}=\frac{PT}{PR}

substitute

\frac{45}{20}=\frac{36}{16}

2.25=2.25 ----> is true

Corresponding sides are proportional

Triangle PQR is similar to Triangle PST

That means

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side QR is parallel side ST

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4 0
3 years ago
The width and length of a rectangle (in feet)are consecutive odd integers. If the length is increased by 5 feet, the area of the
Tresset [83]
Original:
<span>The width and length of a rectangle are consecutive odd integers
</span>so W = x and L = x + 2

<span>If the length is increased by 5 feet, then new L = x + 2 + 5 = x + 7
</span>
A = L x W
60 = (x + 7) x
60 = x^2 + 7x
x^2 + 7x - 60 = 0
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x = 5 and x = -12

From here you have x = W = 5 ft and L = x + 2 = 5 + 2 = 7 feet

Area of original = 5 x 7 = 35

answer 
<span>the area of the original rectangle: </span>35 ft^2


4 0
3 years ago
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