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skelet666 [1.2K]
3 years ago
10

Point A is located at (2, 3) on the coordinate plane. Point A is reflected over the x-axis to form point B and over the y-axis t

o form point C. Then, point A is reflected over both axes to form point D. The four points become vertices of a quadrilateral. What is the most precise name for the quadrilateral formed, and how do you know?

Mathematics
1 answer:
Mademuasel [1]3 years ago
7 0

Answer:

Rectangle

Step-by-step explanation:

Well if point A is on (2,3) and you reflect it over the x axis point B would be located at (2,-3).

Then over the y axis point C would be located at (-2,-3), then reflecting that over the x axis point D is (-2,3)

<em><u>Points</u></em>

__________

A. (2,3)

B. (2,-3)

C. (-2,-3)

D. (-2,3)

__________

So graphing all these points we get a rectangle.

Because it has 4 sides that are 90 degrees and the sides opposite from each other are the same.

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With that information you can determine how far the park is from the football field.

Call h the height of the triangle, x the distance from the park to the football field and y the distance from the park to the home of Kristen.

Using Pithagora's theorem, ou can state this system of equations:

1) From the complet triangle: x^2 + y^2 = (8 + 2)^2 = 10^2 = 100

2) From the triangle whose hypotenuse is the distance from the park to the football field:

x^2 = 8^2 + h^2

3) From the triangle whose hypotenuse is the distance from the park to the home of Kristen:

y^2 = 2^2 + h^2

To solve the system start by subtracting equation 3) from equation 1) =>

x^2 + y^2 = 100
y^2 = 4 + h^2
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x^2 = 100 - 4 - h^2

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Now sum this result to equation 2

x^2 = 96 - h^2
x^2 = 64 + h^2
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2x^2 = 96 + 64

2x^2 = 160

=> x^2 = 80

=> x = 8.94

Answer: 8.94 miles
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