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nordsb [41]
2 years ago
6

The image is below please help I am crying

Mathematics
1 answer:
Veronika [31]2 years ago
7 0

Answer:

Quadrant III

Step-by-step explanation:

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The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if paral
Iteru [2.4K]

The answer is really none of the above, because all of these have divisions by difference in x, and there are perfectly fine rectangles where those will mean dividing by zero.

To do the problem the way they want us to, we note segments with the same slope are parallel (or collinear); segments with slopes which multiply to -1 are perpendicular.

Let's figure out what each choice is trying to tell us by translating it into parallel and perpendicular. Remember A is point 1, ...

A. ((y_4-y_3)/(x_4-x_3)= (y_3-y_2)/(x_3-x_2)) and ((y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2))=-1

translated, that's CD║BC and CD⊥BC - contradictory; second half right

B. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and ((y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1))=-1

CD ║ AB and CD ⊥ AB - only the parallelogram half is right

C. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and (y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2)=-1

CD║AB and CD⊥BC - that's TRUE

D. (y_4-y_3)/(x_4-x_3)= (y_3-y_1)/(x_3-x_1) and (y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1)=-1

CD║AC and CD⊥AB - nope

Answer: C

The way I'd get the proper expression is with the dot product.

A parallelogram is a rectangle when adjacent sides are perpendicular. It only takes one right angle to make them all right.

Two sides are perpendicular when the dot product of their direction vectors is zero. All the answers have y_4 - y_3 so one side is CD. The other side must be BC or AD; AD would give y_4 - y_1 terms which don't appear among the answer, so let's go with BC.

The direction vectors are

D-C = (x_4 - x_3, y_4 - y_3)

C-B = (x_3 - x_2, y_3 - y_2)

For perpendicularity we need a zero dot product:

0 = (D-C)\cdot(C-B) = (x_4 - x_3)(x_3 - x_2) + (y_4 - y_3)(y_3 - y_2)

- (x_4 - x_3)(x_3 - x_2) = (y_4 - y_3)(y_3 - y_2)

That's the correct expression, given it's a parallelogram, to demonstrate it's a rectangle. The divisions make it iffy.

8 0
2 years ago
there are 2,300 licensed dogs in clarkson. A random sample of 50 of the dogs in Clarkson shows that 8 have ID microchips implant
algol [13]
Set up a ratio comparing the sample portion to the whole portion.

x= # of all dogs likely to have chip

Sample: 8 out of 50
Whole: x out of 2,300

8/50= x/2300
cross multiply

(50*x)= (8*2300)
50x= 18400

divide both sides by 50
x= 368


ANSWER: 368 dogs in Clarkson are likely to have a microchip.

Hope this helps! :)
7 0
2 years ago
Read 2 more answers
Gail is 6 years younger than Mark.Let m= Mark’s age which expression equals Gail’s age?
OLEGan [10]
The answer is C M-6
3 0
3 years ago
Can someone help me find x of this triangle
uysha [10]

Answer:

x = 9

Step-by-step explanation:

Sum of a triangle is 180°.

6x + 1 + 6x - 14 + 9x + 4 = 180°

Arrange the like terms together and simply this equation.

6x + 6x + 9x + 1 + 4 - 14 = 180°

21x - 9 = 180°

Shifting '-9' to the other side of the equation gives you '+9'

21x = 180° + 9

21x = 189

Shifting 21 to the other side of the equation (to get x) makes it  ÷21 (multiply)

x = 189 ÷ 21

x = 9

3 0
3 years ago
45^2 ÷ 78 = ????????
elena55 [62]
\frac{(45)^2}{78}

To solve the problem find the value of (45)^2 at first

(45)^2=2025\frac{2025}{78}=25\text{ R75}

The answer is 25 with the remainder 75

25\frac{75}{78}

You can simplify the fraction to be 25/26

25\frac{25}{26}

3 0
1 year ago
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