Question

Find the distance between the points. Give an exact answer and an approximation to three decimal places. (-1,3)and (6,-4)

Answer 1

To calculate the distance between the points (-1,3) and (6,-4), use the distance formula. The exact distance is √98, and the approximation is 9.899 units to three decimal places.

Step-by-step explanation:

To find the distance between two points in the Cartesian plane, you can use the distance formula which is derived from the Pythagorean theorem. Let's calculate the distance between the points (-1,3) and (6,-4).

1. First, subtract the x-coordinates and y-coordinates of the two points separately:
   (6 - (-1)) = 7 and (-4 - 3) = -7.
2. Next, square each of the differences: 7^2 = 49 and (-7)^2 = 49.
3. Add these squares: 49 + 49 = 98.
4. Finally, take the square root of this sum to get the distance: √98, which is the exact answer.
5. To approximate this to three decimal places, √98 ≈ 9.899.

So, the exact distance is √98 units, and the approximation to three decimal places is 9.899 units.