The sides of a square are 3 cm long. One vertex of the square is at (2,0) on a square coordinate grid marked in centimeter units. Which of the following points could also be a vertex of the square?
A. (−4, 0)
B. (0, 1)
C. (1, −1)
D. (4, 1)
E. (5, 0)
Answer (3)
Answer: The required point that could also be a vertex of the square is K(5, 0).
**Step-by-step explanation: **Given that the sides of a square are 3 cm long and one vertex of the square is at (2,0) on a square coordinate grid marked in centimeter units.
We are to select the co-ordinates of the point that could also be a vertex of the square.
To be a vertex of the given square,** the distance between the point and the vertex at (2, 0) must be 3 cm.**
Now, we will be suing the** distance formula** to calculate the lengths of the segment from the point to the vertex (2, 0).
If the point is** F(-4, 0),** then the length of the line segment will be
ℓ = ( − 4 − 2 ) 2 + ( 0 − 0 ) 2 = 6 2 + 0 2 = 6 2 = 6 cm = 3 cm .
If the point is G(0, 1), then the length of the line segment will be
ℓ = ( 0 − 2 ) 2 + ( 1 − 0 ) 2 = 2 2 + 1 2 = 4 + 1 = 5 cm = 3 cm .
If the point is H(1, -1), then the length of the line segment will be
ℓ = ( 1 − 2 ) 2 + ( − 1 − 0 ) 2 = 1 2 + 1 2 = 1 + 1 = 2 cm = 3 cm .
If the point is J(4, 1), then the length of the line segment will be
ℓ = ( 4 − 2 ) 2 + ( 1 − 0 ) 2 = 2 2 + 1 2 = 4 + 1 = 5 cm = 3 cm .
If the point is K(5, 0), then the length of the line segment will be
ℓ = ( 5 − 2 ) 2 + ( 0 − 0 ) 2 = 3 2 + 0 2 = 3 2 = 3 cm .
Thus, the required point that could also be a vertex of the square is K(5, 0).
K (5.0) It's easy just use 2plus3and that's it.
The only point that could also be a vertex of the square is (5, 0), as it is 3 cm away from the vertex at (2, 0). All other options do not satisfy the distance condition. Therefore, the correct answer is option E (5, 0).
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