Question

What is the distance, in coordinate units, between the points (-3, 5) and (6, -2) in the standard (x, y) coordinate plane?

Answer 1

The distance between the points (-3, 5) and (6, -2) on the coordinate plane is approximately 11.4 units, calculated using the distance formula.

Step-by-step explanation:

The distance between the two points (-3, 5) and (6, -2) in the standard (x, y) coordinate plane can be found using the distance formula √((x2 - x1)² + (y2 - y1)²). Applying this formula:

1. 
   
3. Calculate the difference in the x-coordinates: 6 - (-3) = 9.
4. 
   
6. Calculate the difference in the y-coordinates: -2 - 5 = -7.
7. 
   
9. Square these differences: 9² = 81 and (-7)² = 49.
10. 
    
12. Add the squares of the differences: 81 + 49 = 130.
13. 
    
15. Take the square root of the sum to find the distance: √130 ≈ 11.4 units.

So, the distance between the points (-3, 5) and (6, -2) is approximately 11.4 coordinate units.