To find the distance between the two points, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two points form a right triangle with the line joining them as the hypotenuse. To find the length of the line, we need to find the lengths of the two sides.
The length of the horizontal side (the difference in x-coordinates) can be found by subtracting the x-coordinate of one point from the x-coordinate of the other point. In this case, it is 2 - (-2) = 4.
The length of the vertical side (the difference in y-coordinates) can be found by subtracting the y-coordinate of one point from the y-coordinate of the other point. In this case, it is 4 - (-1) = 5.
Now we can use the Pythagorean theorem: hypotenuse^2 = horizontal side^2 + vertical side^2.
Substituting in the values we found, we get: hypotenuse^2 = 4^2 + 5^2 = 16 + 25 = 41.
To find the length of the hypotenuse, we take the square root of both sides: hypotenuse = sqrt(41) ≈ 6.40 (rounded to the nearest hundredth).
Therefore, the length between the two points is approximately 6.40.
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Question
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
5.57
5.57
6:40
3 answers
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.
(1 point)
Responses
7.62
7.62
11
11
8.54
8.54
73
(1 point)
Responses
7.62
7.62
11
11
8.54
8.54
73
To find the length between the two points, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two points form a right triangle with the line joining them as the hypotenuse. We need to find the lengths of the two sides.
The length of the horizontal side (the difference in x-coordinates) can be found by subtracting the x-coordinate of one point from the x-coordinate of the other point. In this case, it is 2 - (-2) = 4.
The length of the vertical side (the difference in y-coordinates) can be found by subtracting the y-coordinate of one point from the y-coordinate of the other point. In this case, it is 4 - (-1) = 5.
Now we can use the Pythagorean theorem: hypotenuse^2 = horizontal side^2 + vertical side^2.
Substituting in the values we found, we get: hypotenuse^2 = 4^2 + 5^2 = 16 + 25 = 41.
To find the length of the hypotenuse, we take the square root of both sides: hypotenuse = sqrt(41) ≈ 6.40 (rounded to the nearest hundredth).
Therefore, the length between the two points is approximately 6.40.
In this case, the two points form a right triangle with the line joining them as the hypotenuse. We need to find the lengths of the two sides.
The length of the horizontal side (the difference in x-coordinates) can be found by subtracting the x-coordinate of one point from the x-coordinate of the other point. In this case, it is 2 - (-2) = 4.
The length of the vertical side (the difference in y-coordinates) can be found by subtracting the y-coordinate of one point from the y-coordinate of the other point. In this case, it is 4 - (-1) = 5.
Now we can use the Pythagorean theorem: hypotenuse^2 = horizontal side^2 + vertical side^2.
Substituting in the values we found, we get: hypotenuse^2 = 4^2 + 5^2 = 16 + 25 = 41.
To find the length of the hypotenuse, we take the square root of both sides: hypotenuse = sqrt(41) ≈ 6.40 (rounded to the nearest hundredth).
Therefore, the length between the two points is approximately 6.40.
3 answers