Example Question - two points
Here are examples of questions we've helped users solve.
Calculating Distance Between Two Points on a Coordinate Plane
The question is asking you to calculate the distance between two points on a coordinate plane, which essentially is asking you to find the length of the hypotenuse of a right triangle formed with these two points as its endpoints. The points provided are (3, 7) and (8, 5). To determine the distance between these two points, you can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Where (x1, y1) and (x2, y2) are the coordinates of the two points. Substitute the coordinates into the formula: \[ d = \sqrt{(8 - 3)^2 + (5 - 7)^2} \] \[ d = \sqrt{(5)^2 + (-2)^2} \] \[ d = \sqrt{25 + 4} \] \[ d = \sqrt{29} \] So, the distance between the two points to the nearest tenth is approximately \(\sqrt{29}\), which is about 5.4 when rounded to the nearest tenth.
Calculating Distance Between Two Points in a Coordinate Plane
To find the distance between two points, we can use the formula for the distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) in the coordinate plane: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] The points given are \( (-3, -4) \) and \( (-10, -9) \). Let's plug these coordinates into the formula: \[ d = \sqrt{(-10 - (-3))^2 + (-9 - (-4))^2} \] \[ d = \sqrt{(-10 + 3)^2 + (-9 + 4)^2} \] \[ d = \sqrt{(-7)^2 + (-5)^2} \] \[ d = \sqrt{49 + 25} \] \[ d = \sqrt{74} \] Now, let's find the square root of 74. \[ d \approx 8.602 \] Rounded to the nearest tenth, the distance is approximately 8.6 units.
Calculating Distance Between Two Points in a Coordinate System
To find the distance between two points in a coordinate system, you can use the distance formula: Distance = √[(x2 - x1)² + (y2 - y1)²] Plugging in the coordinates for the two points (9,2) and (2,9), we get: x1 = 9, y1 = 2 x2 = 2, y2 = 9 Distance = √[(2 - 9)² + (9 - 2)²] Distance = √[(-7)² + (7)²] Distance = √[49 + 49] Distance = √[98] Now, we can round the result to the nearest tenth: Distance ≈ √[98] ≈ 9.899494937 Rounded to the nearest tenth, the distance is approximately 9.9 units.
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