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.
2 answers:
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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Answer:
The answers to the questions about problem 2 are:
- The fraction of the length after Priya stops two times is 3/4.
- The fraction of the length after Priya stops four times is 15/16.
- Priya will never reach the end of the hallway.
Step-by-step explanation:
The explanation about each answer is below:
1. In the first stop, Priya has walked half of the total length, and there would still be half the hallway, however, when she stops the second time, she has walked the half of the half, I mean:
If you add the two values you obtain the total distance traveled by Priya:
And the distance traveled in two stops is 3/4 of the total length of the hallway.
2. With four stops the system is the same, we know with two stops Priya travels 3/4 of the hallway, now with the third stop, she will travel half of the remaining distance:
And in the fourth stop she will travel half of the remaining, I mean:
Now, we add all the values of the distances obtained:
So, the distance traveled by Priya in the fourth stop is 15/16 of the total length of the hallway.
3. How we know, the numbers are infinite, in the same forms the distances, by this reason, how the problem says that Priya walks just half of the distance, she will never reach the end because despite she has very near of the end, she will continue walking just half and ever smaller distances.