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sdas [7]
2 years ago
13

Parallelogram ABCD has vertices: A(-3, 1), B(3, 3), C(4, 0), and D(-2, -2). In two or more complete sentences, explain how you c

an use the coordinates of the vertices to prove that parallelogram ABCD is a rectangle.

Mathematics
2 answers:
mina [271]2 years ago
4 0
You have to shoe that the angles between adjacent sides = 90 degrees. You do do this by showing the adjacent sides are perpendicular  by comparing their slopes. 
raketka [301]2 years ago
3 0

Answer:

Step-by-step explanation:

Remember, the slope of parallel lines is the same, while the slope of perpendicular lines is the negative reciprocal of each other.

We are given that points a(-3,1), b(3,3), c(4,0) and d(-2,-2). Let’s first identify the relationships between the lines that form the sides of rectangle ABCD.

Lines AD and BC are parallel

Lines AB and DC are parallel

Lines AB and AD are perpendicular

Lines BC and DC are perpendicular

Lines AD and BC are parallel, since the two lines share a slope of -3.

Lines AB and DC are parallel, since they both share a slope of 1/3.

Lines CD and BC are perpendicular, since they are the opposite reciprocal of each other. CD has a slope of 1/3. BC has a slope of -3.

Lines DC and AD are perpendicular as well. DC has a slope of 1/3. AD has a slope of -3.

Using this information, we can arrive at the conclusion that parallel lines DC and AB intersect with parallel lines BC and AD. The intersection of these pairs of parallel lines make up the sides of rectangle ABCD, which proves that the vertices of the parallelogram forms a rectangle.

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If you were a colonist in the mid-1770s would you have stood with the Patriots or the Loyalists? Write an argumentative essay in
vekshin1

Answer:

I would have stood with the patriots because British soldiers forcefully entered their homes. They also ramped up taxes over a petty war with France because they couldnt pay it themselves.

The Loyalists were brainwashed to the British king, because they were rich and privileged. So they could pay the very high taxes. This meant these guys didn't actually know how the people felt.

The British also ramped up the price of tea, which the colonists loved, just to be petty because the Patriots did not want to be taxed. Back then, the British were very petty. Now they're just jaded.

But back to the essay: The Patriots had a good cause. They wanted to move on from something chaining them down. The Loyalists did not. And I would want to happily tar some tax collectors. Wouldn't you?

Step-by-step explanation:

5 0
3 years ago
-2 - -4 * -9 = <br> HELP I WILL GIVE BRAINLIEST!
Bess [88]

Answer: -34

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Please help!!!! I only need to do A not B!!! 8 points!!!!
Nadya [2.5K]
2/5+-1/3 please excuse my sloppy writing

8 0
2 years ago
Find the value of the variable in the parallelogram.
patriot [66]
I kind a get the answer for this one but I’m not sure if that’s the correct one but I think your answer will be -6
7 0
2 years ago
See the picture below
mart [117]

Answer:

a) 301.59 cubic centimeters

b) 235.87 square centimeters

Step-by-step explanation:

a)

Volume of ice cream cone is volume of hemisphere PLUS volume of cone.

Volume of Hemisphere = \frac{\frac{4}{3}\pi r^3}{2}

radius is given as 4, so,

Volume of Hemisphere = \frac{\frac{4}{3}\pi r^3}{2}\\=\frac{\frac{4}{3}\pi (4)^3}{2}\\=134.04

Now, Volume of Cone = \frac{1}{3}\pi r^2 h

Where radius is 4 and height is 10, so,

Volume of Cone = \frac{1}{3}\pi r^2 h\\=\frac{1}{3}\pi (4)^2 (10)\\=167.55

Volume of Ice Cream Cone = 134.04 + 167.55 = 301.59 cubic centimeters

b)

Surface area of ice cream cone is surface area of hemisphere PLUS surface area of cone.

Surface Area of Hemisphere = 2\pi r^2\\=2\pi (4)^2\\=100.53

Surface Area of Cone = \pi r^2+\pi rl

We dont need to use the first part, \pi r^2  since it is "inside". We  need to find l, slant height, by using pythagorean theorem on a triangle we can make (bottom right).

4^2 + 10^ 2 = l^2

16 + 100 = l^2

116 = l^2

l = 10.77

Now to find the surface area of cone = \pi rl\\=\pi (4)(10.77)\\=135.34

Surface area of ice cream cone = 100.53 + 135.34 = 235.87 square centimeters

5 0
2 years ago
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