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pogonyaev
3 years ago
13

A polygon has vertices whose coordinates are A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1). Use the midpoint formula to determine w

hether or not the diagonals of polygon ABCD bisect each other. In your final answer, include all of your calculations.
Mathematics
1 answer:
Alenkinab [10]3 years ago
3 0

Answer:

The diagonals of the polygon ABCD bisect each other

Step-by-step explanation:

The given vertices of the polygon are;

A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1)

Given that the vertices of the polygon in clockwise order from the top left corner are ABCD, we have the diagonals as AC and DB

By the midpoint formula, we have;

(x_m , \ y_m) = \left (\dfrac{x_1 + x_2}{2} , \ \dfrac{y_1 + y_2}{2} \right )

Where;

(x_m , \ y_m) = The midpoint coordinates

Therefore, the midpoint of diagonal AC = \left (\dfrac{1 + (-1)}{2} , \ \dfrac{4 + (-4)}{2} \right ) = (0, 0)

The midpoint  of diagonal DB = \left (\dfrac{(-4) +4}{2} , \ \dfrac{1 + (-1)}{2} \right ) = (0, 0)

Therefore, given that the coordinates of the location of the midpoint of the diagonals AC and DB is the same, the diagonals bisect each other

Each diagonal passes through the midpoint of the other diagonal.

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3 years ago
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Answer:

m=\frac{9}{10}

Step-by-step explanation:

To find the slope between any two points, we can use the following slope formula:

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One year on Venus is equivalent to 224.7 days on Earth. How many days on Earth, in decimal from, are equivalent to 9 ½ years on
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By using simple rule of three, a period of 9.5 years on Venus is equivalent to 2134.65 terrestrial days.

<h3>How many terrestrial days are equivalent time in Venus?</h3>

One year on Earth is equivalent to 365.3 days and one year on Venus is equivalent to 224.7 days, the equivalent terrestrial time of 9.5 years on Venus is found by simple rule of three:

x = 9.5 yr × (224.7 days / 1 yr)

x = 2134.65 days

A period of 9.5 years on Venus is equivalent to 2134.65 terrestrial days.

To learn more on simple rule of three: brainly.com/question/15209325

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