Example Question - distance between two points
Here are examples of questions we've helped users solve.
Calculating Distance Between Two Points in a Plane
To find the distance between two points in a plane, you can use the distance formula, which is derived from the Pythagorean theorem. The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] For the points \( (1, -7) \) and \( (-6, 2) \), we can calculate the distance as follows: Let \( x_1 = 1 \), \( y_1 = -7 \), \( x_2 = -6 \), and \( y_2 = 2 \). \[ d = \sqrt{(-6 - 1)^2 + (2 - (-7))^2} \] \[ d = \sqrt{(-7)^2 + (9)^2} \] \[ d = \sqrt{49 + 81} \] \[ d = \sqrt{130} \] \[ d \approx 11.4 \] (rounded to the nearest tenth) So the distance between the points \( (1, -7) \) and \( (-6, 2) \) is approximately 11.4 units.
Calculating Distance Between Two Points
To find the distance between the points (8, 2) and (3, 8), we use the distance formula derived from the Pythagorean theorem: Distance = √[(x2 - x1)² + (y2 - y1)²] Here, (x1, y1) is the point (8, 2) and (x2, y2) is the point (3, 8). Plugging in these values: Distance = √[(3 - 8)² + (8 - 2)²] Distance = √[(-5)² + (6)²] Distance = √[25 + 36] Distance = √61 Distance ≈ 7.8 (rounded to the nearest tenth) So, the distance between the points is approximately 7.8 units.
Finding the Distance between Two Points
To find the distance between the two points (9, 1) and (3, 10), you can use the distance formula, which is derived from the Pythagorean theorem: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Here, \( (x_1, y_1) = (9, 1) \) and \( (x_2, y_2) = (3, 10) \). Plugging in the values: \[ \text{Distance} = \sqrt{(3 - 9)^2 + (10 - 1)^2} \] \[ \text{Distance} = \sqrt{(-6)^2 + (9)^2} \] \[ \text{Distance} = \sqrt{36 + 81} \] \[ \text{Distance} = \sqrt{117} \] Now, simplify this to get the final answer: \[ \text{Distance} = \sqrt{117} \approx 10.82 \] The question asks to round decimals to the nearest tenth: \[ \text{Distance} \approx 10.8 \text{ units} \]
Calculating Distance Between Two Points on a Coordinate Plane
To find the distance between two points on a coordinate plane, you can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \) The two points you have are (2, -7) and (8, -7). Plugging these into the formula gives: \( x_1 = 2, y_1 = -7 \) \( x_2 = 8, y_2 = -7 \) Now compute the distance: \( d = \sqrt{(8 - 2)^2 + (-7 - (-7))^2} \) \( d = \sqrt{(6)^2 + (0)^2} \) \( d = \sqrt{36 + 0} \) \( d = \sqrt{36} \) \( d = 6 \) So the distance between the points (2, -7) and (8, -7) is 6 units.
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