Question
A square is made by conecting points:
A: (-7,6)
B: (-2, -6)
C: (10, -1)
D: (5, 11)
what is the side lengths?
what is the area of the square?
A: (-7,6)
B: (-2, -6)
C: (10, -1)
D: (5, 11)
what is the side lengths?
what is the area of the square?
Answers
GPT 3.5
To find the side lengths of the square, we need to find the distances between each pair of consecutive points.
The distance formula between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we find the distances between the points:
AB = √((-2 - (-7))^2 + (-6 - 6)^2) = √(5^2 + 12^2) = √(25 + 144) = √169 = 13
BC = √(10 - (-2))^2 + (-1 - (-6))^2 = √(12^2 + 5^2) = √(144 + 25) = √169 = 13
CD = √(5 - 10)^2 + (11 - (-1))^2 = √((-5)^2 + 12^2) = √(25 + 144) = √169 = 13
AD = √(5 - (-7))^2 + (11 - 6)^2 = √(12^2 + 5^2) = √(144 + 25) = √169 = 13
Since all sides of the square have equal length, we can conclude that the side length of the square is 13 units.
To find the area of the square, we can use the formula A = side length ^2
A = 13^2 = 169 square units
Therefore, the side lengths of the square are 13 units and the area of the square is 169 square units.
The distance formula between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we find the distances between the points:
AB = √((-2 - (-7))^2 + (-6 - 6)^2) = √(5^2 + 12^2) = √(25 + 144) = √169 = 13
BC = √(10 - (-2))^2 + (-1 - (-6))^2 = √(12^2 + 5^2) = √(144 + 25) = √169 = 13
CD = √(5 - 10)^2 + (11 - (-1))^2 = √((-5)^2 + 12^2) = √(25 + 144) = √169 = 13
AD = √(5 - (-7))^2 + (11 - 6)^2 = √(12^2 + 5^2) = √(144 + 25) = √169 = 13
Since all sides of the square have equal length, we can conclude that the side length of the square is 13 units.
To find the area of the square, we can use the formula A = side length ^2
A = 13^2 = 169 square units
Therefore, the side lengths of the square are 13 units and the area of the square is 169 square units.