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Anarel [89]
3 years ago
14

The vertices of a quadrilateral are A(-1, 6), B(-2, 4), C(2, 2), and D(3, 4). Write a paragraph proof to determine whether quadr

ilateral ABCD is a rectangle.
Mathematics
2 answers:
Katarina [22]3 years ago
6 0
A rectangle is a quadrilateral with either two opposite sides equal and parallel to each other. That is AB is parallel and equal to CD and AD parallel and equal to BC. Parallel lines have equal slopes.
Thus, AB slope is 2, while that of CD is also 2, therefore they are parallel to each other. In addition the modulus of AB and that of CD is the same thus they are equal in length.
AD slope is -1/2 while that of BC is also -1/2 therefore the two are parallel to each other. In addition they are equal in length therefore they are equal in length. 
Moreover AB is perpendicular to BC and AD (product of slope of two perpendicular lines is -1)
Therefore, it can be concluded that Quadrilateral ABCD is a rectangle.

Ivanshal [37]3 years ago
5 0

Answer:

I am given that the vertices of quadrilateral ABCD are A(-1, 6), B(-2, 4), C(2, 2), and D(3, 4). The slope formula applied to each pair of adjacent vertices gives the slopes (m) of the sides:




Because line segments with equal slopes are parallel, segment AB is parallel to segment CD and segment BC is parallel to segment DA.


Multiplying the slopes of one pair of adjacent sides, I find that .


If the product of the slopes of two segments is -1, then they are perpendicular. Since both pairs of opposite sides have been proven parallel, proving one pair of adjacent sides perpendicular implies that the other pair of adjacent sides are also perpendicular. Therefore, by definition, quadrilateral ABCD is a rectangle.

Step-by-step explanation:


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How can you use number patterns to find the least common factor
Aleks04 [339]

Answer:

The correct answer is: 360.

Explanation:

First we can express 120 as follows:

2 * 2 * 2 * 3 * 5 = 120

You can get the above multiples as follows:

120/2 = 60

60/2 =30

30/2 = 15

15/3 = 5 (Since 15 cannot be divisible by 2, so we move to the next number)

5/5 = 1

Take all the terms in the denominator for 120, you would get: 2 * 2 * 2 * 3 * 5 --- (1)

Second we can express 360 as follows:

360/2 = 180

180/2 = 90

90/2 =45

45/3 = 15 (Since 45 cannot be divisible by 2, so we move to the next number)

15/3 = 5

5/5 = 1

Take all the terms in the denominator for 360, you would get: 2 * 2 * 2 * 3 * 3 * 5 --- (2)

Now in (1) and (2) consider the common terms once and multiple that with the remaining:

2*2*2*3*5 = Common between the two

3 = Remaining

Hence (2*2*2*3*5) * (3) = 360 = LCM (answer)

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3 years ago
What is 312/17 in simplest form.
My name is Ann [436]
312/17
= (306+6)/ 17
= 306/17+ 6/17
= 18+ 6/17
= 18 6/17

The final answer is 18 6/17~
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Step-by-step explanation:


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