Use the image to answer the question.
A graph shows quadrant 1 with the x-axis and y-axis ranging from 0 to positive 9. Data points marked are at left parenthesis 3 comma 2 right parenthesis, and left parenthesis 7 comma 8 right parenthesis. A straight line joins the two points forming a positive slope.
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.
(1 point)
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Unfortunately, without the image it is not possible to accurately answer the question. Please provide the image so that the question can be properly addressed.
To find the length between the two points, we can use the Distance Formula, which is a variation of the Pythagorean Theorem.
The Distance Formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's label the coordinates as follows:
Point 1: (x1, y1) = (3, 2)
Point 2: (x2, y2) = (7, 8)
Now, we can substitute these values into the formula:
d = √((7 - 3)^2 + (8 - 2)^2)
Simplifying further:
d = √((4)^2 + (6)^2)
d = √(16 + 36)
d = √52
Calculating the square root, rounded to the nearest hundredth:
d ≈ 7.21
Therefore, the length between the two points is approximately 7.21 units.
To find the length between two points using the Pythagorean Theorem, we need to calculate the distance between their x-coordinates and y-coordinates.
Let's label the first point as A(3, 2) and the second point as B(7, 8).
The x-coordinate difference between the two points is given by the equation:
Δx = x2 - x1 = 7 - 3 = 4
Similarly, the y-coordinate difference is:
Δy = y2 - y1 = 8 - 2 = 6
Now, we can use the Pythagorean Theorem, which states that in a right-angled 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 distance between the two points is the hypotenuse of a right-angled triangle, and the x and y-coordinate differences are the other two sides.
Therefore, we have:
Distance^2 = (Δx)^2 + (Δy)^2
Substituting the values, we get:
Distance^2 = 4^2 + 6^2 = 16 + 36 = 52
To find the actual distance, we take the square root on both sides of the equation:
Distance = √52 ≈ 7.21
Rounding the answer to the nearest hundredth, the length between the two points is approximately 7.21 units.