Question

How would you determine the distance between (6,8) and (2,-3)

Answer 1

To calculate the distance between two points, such as (6,8) and (2,-3), use the distance formula, which is the square root of the sum of the squares of the differences in x and y coordinates. After performing the calculations, the distance between the points is approximately 11.7 units.

Step-by-step explanation:

To determine the distance between two points, in this case (6,8) and (2,-3), we use the distance formula derived from the Pythagorean theorem. The distance formula is √((x2-x1)2 + (y2-y1)2), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this example, (x1, y1) is (6,8), and (x2, y2) is (2,-3).

To find the distance, follow these steps:

1. Subtract the x-values: 2 - 6 = -4.
2. Subtract the y-values: -3 - 8 = -11.
3. Square each difference: (-4)2 = 16 and (-11)2 = 121.
4. Add the squares: 16 + 121 = 137.
5. Take the square root of the sum: √137 ≈ 11.7.

Therefore, the distance between the two points is approximately 11.7 units.