Question

The points (6,7) and (-5,-3) are shown on a coordinate grid. What is the distance in units between the points?

Answer 1

The distance between the points (6,7) and (-5,-3) is found using the distance formula and is approximately 14.87 units.

Step-by-step explanation:

To find the distance between two points in a coordinate grid, we use the distance formula, which is derived from the Pythagorean theorem. The formula is √((x2 - x1)2 + (y2 - y1)2). For the points (6,7) and (-5,-3), the calculation is as follows:

1. Subtract the x-coordinates: (6 - (-5)) = 11.
2. Subtract the y-coordinates: (7 - (-3)) = 10.
3. Square each result: 112 = 121 and 102 = 100.
4. Add the squares together: 121 + 100 = 221.
5. Take the square root of the sum: √221 ≈ 14.87.
   

Therefore, the distance between the two points is approximately 14.87 units.