A square has a perimeter of 12 units. One vertex is at the point left-parenthesis negative 1 comma 1 right-parenthesis, and another vertex is at the point left-parenthesis 2 comma 4 right-parenthesis. Which of the following points could be another vertex?
A. (1,2)
B. (2,1)
C. (1,-2)
D. (2,-1)
(You don't need to help but it would be nice)
These are the answers for the test.
1. A
2. C
3. A
4. C
5. C, D
6. C
7. B
8. A
9. A, C
10. A, C
Erin is correct!!!
Erin is correct
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Erin in correct thx a lot!!!
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OMG Erin thx so much!!!
To solve this problem, we need to first calculate the length of one side of the square, and then check the four given points to see if any of them can be another vertex of the square.
To calculate the length of one side of the square, we divide the perimeter of the square by 4 since a square has four sides of equal length.
Perimeter of the square = 12 units
Length of one side = Perimeter / 4 = 12 / 4 = 3 units
Now let's calculate the distance between the two given vertices: (-1, 1) and (2, 4). We can use the distance formula, which is the square root of the sum of the squared differences in the x-coordinates and y-coordinates.
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Distance = sqrt((2 - (-1))^2 + (4 - 1)^2)
= sqrt(3^2 + 3^2)
= sqrt(18)
= 3sqrt(2)
Since a square has all sides of equal length, each side must be equal to 3 units. Therefore, the distance between any two vertices of the square must also equal 3 units.
Now let's calculate the distance between the given vertex (-1, 1) and each of the given points to see if any of them have a distance of 3 units.
Distance between (-1, 1) and (1, 2):
= sqrt((1 - (-1))^2 + (2 - 1)^2)
= sqrt(2^2 + 1^2)
= sqrt(5)
≈ 2.24 units
Distance between (-1, 1) and (2, 1):
= sqrt((2 - (-1))^2 + (1 - 1)^2)
= sqrt(3^2 + 0^2)
= 3 units
Distance between (-1, 1) and (1, -2):
= sqrt((1 - (-1))^2 + (-2 - 1)^2)
= sqrt(2^2 + (-3)^2)
= sqrt(13)
≈ 3.61 units
Distance between (-1, 1) and (2, -1):
= sqrt((2 - (-1))^2 + (-1 - 1)^2)
= sqrt(3^2 + (-2)^2)
= sqrt(13)
≈ 3.61 units
From the calculations, we can see that the only point with a distance of 3 units from the given vertex (-1, 1) is (2, 1).
Therefore, the correct answer is B. (2, 1)
what are all those words? You clearly know how to write points in the choices. So why all the garbage up front? Try saying
A square has a perimeter of 12 units. One vertex is at the point (-1,1), and another vertex is at the point (2,4). Which of the following points could be another vertex?
Now, the line from (-1,1) to (2,4) has a slope of 1
So, the line from either point to another vertex must have a slope of -1.
Just check the choices to see which works.
A lot easier, though, is just to get out some graph paper and plot the two pints and all of the choices. It should be clear right away which is correct.