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vaieri
2 months 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:
Leona [12.6K]2 months ago
4 0
You must demonstrate that the angles formed by adjacent sides equal 90 degrees. This can be established by showing that the adjacent sides are perpendicular through a comparison of their slopes. 
Leona [12.6K]2 months ago
3 0

Answer:

Step-by-step explanation:

Keep in mind that parallel lines have identical slopes, while the slopes of perpendicular lines are negative reciprocals of one another.

We have the points a(-3,1), b(3,3), c(4,0), and d(-2,-2). First, let's identify the relationships among the lines that create the sides of rectangle ABCD.

Lines AD and BC are parallel.

Lines AB and DC also run parallel.

Lines AB and AD are perpendicular.

Lines BC and DC are perpendicular as well.

Lines AD and BC share a slope of -3, indicating they are parallel.

Lines AB and DC have a slope of 1/3, confirming their parallel nature.

Lines CD and BC are perpendicular due to their slopes being negative reciprocals—CD has a slope of 1/3, and BC has a slope of -3.

Similarly, lines DC and AD are also perpendicular, with DC at 1/3 and AD at -3.

With this information, we conclude that the parallel lines DC and AB intersect with the parallel lines BC and AD. The intersection points of these parallel line pairs form the sides of rectangle ABCD, thus proving that the coordinates of the parallelogram indeed create a rectangle.

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What is the solution to the system of equations? y = A system of equations. Y equals StartFraction one-third EndFraction minus 1
lawyer [12517]

Response:

(6,-8).

Detailed explanation:

We have a set of equations provided. Our task is to find the solution for this system.

y=\frac{1}{3}x-10...(1)

2x+y=4...(2)

Starting from equation (2), we will derive:

y=4-2x...(2)

Next, by inserting this value into equation (1), we will achieve:

4-2x=\frac{1}{3}x-10

After multiplying both sides by 3, we will arrive at:

3\cdot 4-3\cdot 2x=3\cdot \frac{1}{3}x-3\cdot 10

12-6x=x-30

12-6x-x=x-x-30

12-7x=-30

12-12-7x=-30-12

-7x=-42

\frac{-7x}{-7}=\frac{-42}{-7}

x=6

Now substituting this back into equation (2), we will find:

y=4-2(6)

y=4-12

y=-8

Thus, the solution to our specified set of equations is (6,-8).

4 0
2 months ago
Read 2 more answers
Find three solutions for the linear equation 4x −3y = 1, and plot the solutions as points on a coordinate plane.
lawyer [12517]

Answer:

(1, 1), (2, 2.333) and (3, 3.666).

Step-by-step explanation:

To solve this equation, we can select various values for x and then compute the corresponding y values.

<pFor instance, when x = 1, we find:

4*1 - 3y = 1

3y = 3

y = 1

When x = 2, we discover:

4*2 - 3y = 1

3y = 7

y = 2.333

Then for x = 3, we have:

4*3 - 3y = 1

3y = 11

y = 3.666

Therefore, the coordinates we will plot are (1, 1), (2, 2.333), and (3, 3.666).

Refer to the attached image for the plot.

4 0
2 months ago
A set of notations (SSS, SAS, ASA and RHS) is used to describe/prove
Svet_ta [12734]

Detailed breakdown:

locate the triangles

5 0
3 months ago
Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a
zzz [12365]

Answer:

Step-by-step explanation:

It has been established that the count of drivers traveling between a specific origin and destination in a certain time frame follows a Poisson distribution with a mean μ = 20 (as indicated in the article "Dynamic Ride Sharing: Theory and Practice"†).

a) P(X\leq 15) = 0.1565=0.157

b) P(X>26) =1-F(26)\\= 1-0.9221\\=0.0779=0.078

c) P(15\leq x\leq 26)\\=F(26)-F(14)\\=0.9221-0.1049\\=0.8172=0.817

d) 2 standard deviations = 2(20) = 40

Thus, this means the range for 2 standard deviations is

20-40, 20+40

which equates to (0,60)

P(0

5 0
2 months ago
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