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sdas [7]
3 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]3 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]3 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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Our club has 25 members, and wishes to pick a president, secretary, and treasurer. In how many ways can we choose the officers,
Rus_ich [418]

Answer:

13800

Step-by-step explanation:

The order of the members is important (because each selected member will receive a different position), thus we then need to use the definition of permutation.

There are 25 members, of which 3 are selected.

\begin{array}{l}n=25 \\r=3\\end{array}

Evaluate the definition of a combination:

P(25,3)=\frac{25 !}{(25-3) !}=\frac{25 !}{22 !}=25 \cdot 24 \cdot 23=13800

8 0
3 years ago
Beth estimates her expenditures for transportation as follows: May, $91; June, $122; July $478. What is her estimated average mo
kipiarov [429]

Answer:

around 230

Step-by-step explanation:

91+122+478=691

691÷3= 230.33333333

4 0
3 years ago
How do i calculate the first quartile and the third quartile??? <br> !!!please help!!!
diamong [38]

Answer: The Median: 78, The First Quartile: 63, and The Third Quartile: 99

Step-by-step explanation: Ok, so let's put the data set from least to greatest....

(63, 63, 76,) (77, 79,) (84, 99, 99)

First Quartile              Third Quartile

First, let's find the median, since you made a little mistake...

77 + 79 = 156

156 ÷ 2 = 78

The median is 78!

Now, let's determine the first quartile and the third quartile.

For the the first quartile/third quartile it'll be the middle number, if it's even we'll do the same extra step just like we'll do for the median. In this case it's not even therefore...

First Quartile: 63

Third Quartile: 99

I hope this helps!

5 0
3 years ago
Solve the equation using the quadratic formula 3x^2 =2(2x+1)
Nadusha1986 [10]
Step 1: Make equation equal to Zero

3x^2 = 4x + 2


3x^2 - 4x - 2 


Step 2: use equation

a= 3 b = -4 c= -2 

after plugging in answer should be

(2 + or - sqrt 10) / 3 


3 0
3 years ago
Read 2 more answers
I have no idea what to do.<br> Would appreciate help.
miskamm [114]
The anser is 20 that what i think
4 0
3 years ago
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