what is the distanace between the origin and the point (5,-19)
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The distance between two points, P1(x1,y1) and P2(x2,y2) can be calculated by the formula:
D=√((x2-x1)² + (y2-y1)²)
In the given case,
The origin is P1(0,0), and the given point is P2(5,-19).
The distance between them is therefore:
D = √((5-0)²+(19-0)²)
Can you take it from here?
To determine the distance between the origin (0,0) and the point (5,-19), we can use the distance formula. The distance formula is a mathematical rule that allows us to calculate the straight-line distance between two points in a coordinate system.
The distance formula is derived from 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 two sides of the right-angled triangle are the horizontal distance (x-coordinate) and the vertical distance (y-coordinate) between the two points.
To find the distance, follow these steps:
1. Determine the horizontal distance: Subtract the x-coordinate of the origin (0) from the x-coordinate of the point (5), which gives us 5 - 0 = 5.
2. Determine the vertical distance: Subtract the y-coordinate of the origin (0) from the y-coordinate of the point (-19), which gives us -19 - 0 = -19.
3. Square the horizontal distance: Multiply the horizontal distance (5) by itself, 5^2 = 25.
4. Square the vertical distance: Multiply the vertical distance (-19) by itself, (-19)^2 = 361.
5. Add the squared values: Add the squared horizontal distance (25) to the squared vertical distance (361), 25 + 361 = 386.
6. Take the square root: To find the distance, take the square root of the sum, sqrt(386).
Therefore, the distance between the origin (0,0) and the point (5,-19) is approximately sqrt(386).