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
1 answer:
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 so one side is CD. The other side must be BC or AD; AD would give
terms which don't appear among the answer, so let's go with BC.
The direction vectors are
For perpendicularity we need a zero dot product:
That's the correct expression, given it's a parallelogram, to demonstrate it's a rectangle. The divisions make it iffy.
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Given:
The conversions from meter to inches and inches to meter are shown in part A of model 2.
The conversions from liters to quarts and quarts to liters are shown in part B of model 2.
Required:
To find the relationship between the conversion factors used in Part A of Model 2.
To find the relationship in the the conversion factors used in Part B of Model 2.
Explanation:
We have given that 1 meter = 39.4 inches.
Thus, from the calculations shown in part A of model 2, we can conclude that the quantity from meters to inches is converted as:
Thus, 1.5 m =59 inches.
Also, the quantity from inches to meters is converted as:
Hence, 59 in = 1.5 m.
Next,
We have 1 L = 1.06 qt.
Thus, from the calculations shown in part B of model 2, we can conclude that the quantity from quarts to liters is converted as:
Thus, 186 quarts = 175 L.
Also, the quantity from liters to quarts is converted as:
Hence, 175 L = 186 qt.
Final Answer:
We conclude that:
While converting from meters to inches, we multiply the quantity 1.5 by the equality quantity given.
While converting from incehs to meters, we divide the quantity 59 by the equality quantity given.
Also, While converting from quarts to liters, we divide the quntity 186 by the equality quantity given.
While converting from liters to quarts, we multiply the quntity 175 by the equality quantity given.
Answer:
Ok here
Step-by-step explanation:
