To find the length between the two points (3, 2) and (7, 8), we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
Let's consider the two points as the vertices of a right triangle. The legs of the triangle are the horizontal distance (change in x) and the vertical distance (change in y) between the points. The hypotenuse is the straight line joining the two points.
Using the given points, we have:
Change in x = 7 - 3 = 4
Change in y = 8 - 2 = 6
Applying the Pythagorean Theorem, the length of the hypotenuse (distance between the two points) can be found as follows:
hypotenuse^2 = (change in x)^2 + (change in y)^2
hypotenuse^2 = 4^2 + 6^2
hypotenuse^2 = 16 + 36
hypotenuse^2 = 52
To find the length of the hypotenuse, we take the square root of 52:
hypotenuse ≈ √52 ≈ 7.21
Therefore, the length between the two points (3, 2) and (7, 8), rounded to the nearest hundredth, is approximately 7.21.
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.
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