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Explanation The given points (2,2) and (6,2) lie on the same horizontal line. The distance between two points on a horizontal line is equal to the difference in their x-coordinates. In this case, the x-coordinates of both points are 2 and 6 respectively. The difference between these two values is 4, so the distance between the points is 4 units.
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2.
Find the distance between (-1,3) and (2,-1).
Explanation The distance between two points in a coordinate plane can be found using the distance formula, which is derived from the Pythagorean theorem. The formula is: d = √((x2 - x1)^2 + (y2 - y1)^2). In this case, the coordinates of the two points are (-1,3) and (2,-1). Plugging these values into the formula, we get d = √((2 - (-1))^2 + (-1 - 3)^2) = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5. Therefore, the distance between the two points is 5 units.
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3.
Find the distance between (-3,-2) and (5,4).
Explanation The distance between two points in a coordinate plane can be found using the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and the y-coordinates. In this case, the x-coordinate difference is 5 - (-3) = 8, and the y-coordinate difference is 4 - (-2) = 6. The sum of the squares of these differences is 8^2 + 6^2 = 64 + 36 = 100. Taking the square root of 100 gives us the distance between the two points, which is 10.
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4.
Find the distance between (-6,-3) and (6,6).
Explanation The distance between two points in a coordinate plane can be found using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of the difference between the x-coordinates squared plus the difference between the y-coordinates squared. Applying this formula to the given points (-6, -3) and (6, 6), we get the square root of ((6 - (-6))^2 + (6 - (-3))^2) = sqrt(12^2 + 9^2) = sqrt(144 + 81) = sqrt(225) = 15.
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5.
Find the distance between (-8,2) and (4,7).
Explanation The distance between two points in a coordinate plane can be found using the distance formula, which is derived from the Pythagorean theorem. The formula is: √((x2 - x1)^2 + (y2 - y1)^2). In this case, the coordinates of the two points are (-8,2) and (4,7). Plugging these values into the formula, we get: √((4 - (-8))^2 + (7 - 2)^2) = √((12)^2 + (5)^2) = √(144 + 25) = √169 = 13. So, the distance between the two points is 13.
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6.
Find the distance between (-2,2) and (10,11).
Explanation The distance between two points in a coordinate plane can be found using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of the difference of the x-coordinates squared plus the difference of the y-coordinates squared. In this case, the x-coordinates are -2 and 10, and the y-coordinates are 2 and 11. Plugging these values into the distance formula, we get the square root of (-2 - 10)^2 + (2 - 11)^2, which simplifies to the square root of 144 + 81, or the square root of 225. The square root of 225 is 15, so the distance between the two points is 15.
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7.
Find the distance between (-10,8) and (-2,-7).
Explanation The distance between two points in a coordinate plane can be found using the distance formula: √((x2 - x1)^2 + (y2 - y1)^2). Applying this formula to the given points (-10,8) and (-2,-7), we have √((-2 - (-10))^2 + (-7 - 8)^2) = √(8^2 + (-15)^2) = √(64 + 225) = √289 = 17. Therefore, the distance between the two points is 17.
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8.
Find the distance between (-2,-10) and (-8,-2).
Explanation The distance between two points in a coordinate plane can be found using the distance formula, which is the square root of the sum of the squares of the differences between the x-coordinates and y-coordinates of the points. In this case, the x-coordinate difference is (-8) - (-2) = -6, and the y-coordinate difference is (-2) - (-10) = 8. Squaring these differences and summing them gives (-6)^2 + 8^2 = 36 + 64 = 100. Taking the square root of 100 gives the distance of 10.
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9.
Find the distance between (-5,-3) and (7,6).
Explanation The distance between two points in a coordinate plane can be found using the distance formula, which is derived from the Pythagorean theorem. The formula is: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). In this case, the coordinates are (-5, -3) and (7, 6). Plugging these values into the formula, we get d = sqrt((7 - (-5))^2 + (6 - (-3))^2) = sqrt(12^2 + 9^2) = sqrt(144 + 81) = sqrt(225) = 15. Therefore, the distance between the two points is 15 units.
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10.
Find the distance between (-2,-10) and (10,6).
Explanation The distance between two points can be found using the distance formula, which is derived from the Pythagorean theorem. In this case, the x-coordinates of the two points are -2 and 10, and the y-coordinates are -10 and 6. By substituting these values into the distance formula, we get the square root of ((10 - (-2))^2 + (6 - (-10))^2), which simplifies to the square root of (12^2 + 16^2). Evaluating this expression gives us the square root of (144 + 256), which is equal to the square root of 400. The square root of 400 is 20, so the distance between the two points is 20.
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