Use the image to answer the question.
A graph shows quadrant 1 with the x-axis and y-axis ranging from 0 to positive 5. Data points marked are point A at left parenthesis 1 comma 2 right parenthesis, point B at left parenthesis 3 comma 2 right parenthesis, point C at left parenthesis 3 comma 4 right parenthesis, and point D at left parenthesis 1 comma 4 right parenthesis. A line joins points A to B, B to C, C to D, and D to A, forming a rectangle.
Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary.
(1 point)
Responses
4.24
4.24
2.83
2.83
8
8
4
To find the length of the diagonal of the square, we can use the Pythagorean Theorem. The diagonal of a square is the hypotenuse of a right triangle formed by the sides of the square.
In this case, the length of one side of the square is the length of the line segment joining points A and B, which is 2 units. Thus, the length of both sides of the square is 2 times the square root of 2 (since it is a right isosceles triangle).
Using the Pythagorean Theorem, we can find the length of the diagonal of the square:
(diagonal)^2 = (side)^2 + (side)^2
(diagonal)^2 = (2√2)^2 + (2√2)^2
(diagonal)^2 = 4(√2)^2 + 4(√2)^2
(diagonal)^2 = 4(2) + 4(2)
(diagonal)^2 = 8 + 8
(diagonal)^2 = 16
diagonal = √16
The length of the diagonal of the square is 4 units. Therefore, the correct answer is 4
Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3). Round your answer to the nearest hundredth, if necessary.(1 point)
Responses
2.65
2.65
4.58
4.58
5.39
5.39
29
To find the length between (2, 5) and (7, 3), we can use the Pythagorean Theorem. The two given points represent the coordinates (x₁, y₁) and (x₂, y₂) of the endpoints of a line segment.
The length of the line segment can be found using the formula:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Plugging in the values, we have:
distance = √((7 - 2)² + (3 - 5)²)
= √((5)² + (-2)²)
= √(25 + 4)
= √29
Rounding to the nearest hundredth, the length between the two points is approximately 5.39. Therefore, the correct answer is 5.39.
Apply the Pythagorean Theorem to find the length between (−1, 6) and (5, −2). Round your answer to the nearest hundredth, if necessary.(1 point)
Responses
10
10
9.22
9.22
100
100
14
To find the length between (-1, 6) and (5, -2), we can use the Pythagorean Theorem. The two given points represent the coordinates (x₁, y₁) and (x₂, y₂) of the endpoints of a line segment.
The length of the line segment can be found using the formula:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Plugging in the values, we have:
distance = √((5 - (-1))² + (-2 - 6)²)
= √((6)² + (-8)²)
= √(36 + 64)
= √100
= 10
Rounding to the nearest hundredth, the length between the two points is 10. Therefore, the correct answer is 10.
Use the image to answer the question.
A graph shows four quadrants with the x-axis and y-axis both ranging from negative 5 to positive 5 in increments of 1. Unlabeled data points marked are at left parenthesis negative 2 comma negative 1 right parenthesis, and at left parenthesis 2 comma 4 right parenthesis. A straight line joins the two lines with a positive slope.
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.
(1 point)
Responses
9
9
41
41
6:40
6:40
5.57
To find the length between the two points (-2, -1) and (2, 4), we can use the Pythagorean Theorem. The two given points represent the coordinates (x₁, y₁) and (x₂, y₂) of the endpoints of a line segment.
The length of the line segment can be found using the formula:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Plugging in the values, we have:
distance = √((2 - (-2))² + (4 - (-1))²)
= √((4)² + (5)²)
= √(16 + 25)
= √41
Rounding to the nearest hundredth, the length between the two points is approximately 6.40. Therefore, the correct answer is 6.40.
Use the image to answer the question.
A graph shows four quadrants with the x-axis and y-axis both ranging from negative 5 to positive 5 in increments of 1. Data points marked are point A at left parenthesis 2 comma negative 3 right parenthesis, and point B at left parenthesis 5 comma 5 right parenthesis.
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.
(1 point)
Responses
73
73
7.62
7.62
8.54
8.54
11
To find the length between the two points (2, -3) and (5, 5), we can use the Pythagorean Theorem. The two given points represent the coordinates (x₁, y₁) and (x₂, y₂) of the endpoints of a line segment.
The length of the line segment can be found using the formula:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Plugging in the values, we have:
distance = √((5 - 2)² + (5 - (-3))²)
= √((3)² + (8)²)
= √(9 + 64)
= √73
Rounding to the nearest hundredth, the length between the two points is approximately 8.54. Therefore, the correct answer is 8.54.