On a coordinate plane, 2 quadrilaterals are shown. Quadrilateral A B C D has points (2, negative 2), (4, negative 2), (3, negative 4), and (1, negative 4). Quadrilateral J K L M has points (4, negative 4), (8, negative 4), (6, negative 9), and (2, negative 9).
Is quadrilateral JKLM the result of a dilation of quadrilateral ABCD by a scale factor of 2? Why or why not?
Yes, because sides JK and ML are twice as long as sides AB and DC.
Yes, because both figures are parallelograms, so corresponding sides are parallel.
No, because sides JK and ML are not twice as long as sides AB and DC.
No, because sides JM and KL have different slopes from sides AD and BC.
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which of the following will have a negative result
A -8-(-10)
B 12-14
C 7-(-3)
A -8-(-10) will have a positive result because subtracting a negative number is the same as adding its positive value.
B 12-14 will have a negative result because 14 is bigger than 12, so you will end up with a negative difference.
C 7-(-3) will have a positive result because subtracting a negative number is the same as adding its positive value.
The difference of two positive integers is_____ negative
A always
B sometimes
C never
C never.
The difference of two positive integers will always be a positive integer or zero. It cannot be negative.
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You're welcome!
To determine if quadrilateral JKLM is the result of a dilation of quadrilateral ABCD by a scale factor of 2, we need to compare the corresponding sides of the two quadrilaterals.
Let's calculate the lengths of the corresponding sides:
- Side AB: The distance between points (2, -2) and (4, -2) is 2 units.
- Side DC: The distance between points (1, -4) and (3, -4) is 2 units.
- Side JK: The distance between points (4, -4) and (8, -4) is 4 units.
- Side ML: The distance between points (2, -9) and (6, -9) is 4 units.
From the calculations, we can see that the lengths of sides AB and DC are both 2 units, while the lengths of sides JK and ML are both 4 units. Therefore, sides JK and ML are indeed twice as long as sides AB and DC.
Based on this, we can conclude that quadrilateral JKLM is the result of a dilation of quadrilateral ABCD by a scale factor of 2. Therefore, the correct answer is:
Yes, because sides JK and ML are twice as long as sides AB and DC.
You should know how to find the slope of line segments given the endpoints
you should know how to find the length of a line given the endpoints.
Did you perform the steps needed ??
hint:
(2,-2) ----> (4,-2) , looks like the coordinates doubled
(4,-2) ---> (8, -4), that's nice
(3, -4) ----> (6, -9), oops, was expecting (6, -8) , mmmhhhh
try the last one
draw a conclusion
Of course you should have made a sketch and things would be obvious.