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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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How do I do this, I really need some help
meriva
You solve for x and get x<-2 or x>= -1/2 and then graph

4 0
3 years ago
A coin collector has $45 in just dimes and quarters in a piggy bank he counted all the coins and there are 240 total how many ea
Whitepunk [10]

Answer:

The number of <u>dimes are 100</u> and number of <u>quarters are 140.</u>

Step-by-step explanation:

Let the number of dimes be 'd' and quarters be 'q'.

Given:

The sum of amount is $45.

The total number of coins are 240.

1 dime = $0.10

∴ 'd' dimes = \$0.10d

1 quarter = $0.25

∴ 'q' quarters = \$0.25q

Now, as per question:

d+m=240-----1\\0.1d+0.25q=45---2

Multiplying equation (1) by -0.1 and adding the result to equation (2), we get:

-0.1d-0.1q=240\times -0.1\\-0.1d-0.1q=-24\\0.1d+0.25q=45\\-----------\\0.15q=21\\q=\frac{21}{0.15}=140\\\\d=240-q=240-140=100

Therefore, the number of dimes are 100 and number of quarters are 140.

7 0
3 years ago
The graph shows a line and two similar triangles.
Tanzania [10]

Answer: B. Y=2/3x

Step-by-step explanation:

4 0
3 years ago
On a coordinate plane, 4 points are plotted. The points are (1, 4), (2, 6), (3, 9), (4, 13.5). Which statements are true for the
olga55 [171]

Answer:

A, C, and E

Step-by-step explanation:

4 0
3 years ago
What is the slope of this line?
sergiy2304 [10]

Answer: 2/1

Step-by-step explanation:

2/1 because you use rise/run which is moving up 2 units from (0,3) to (0,5) and then moving right 1 unit to (1,5)

8 0
2 years ago
Read 2 more answers
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