SOLUTION: What is the distance between the points (23, -33) and (4, 9)? If necessary, round your answer to two decimal places.

Algebra ->  Length-and-distance -> SOLUTION: What is the distance between the points (23, -33) and (4, 9)? If necessary, round your answer to two decimal places.       Log On


   

Question 458611: What is the distance between the points (23, -33) and (4, 9)? If necessary, round your answer to two decimal places.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Note: is the first point . So this means that x%5B1%5D=23 and y%5B1%5D=-33.
Also, is the second point . So this means that x%5B2%5D=4 and y%5B2%5D=9.


d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 Start with the distance formula.


d=sqrt%28%2823-4%29%5E2%2B%28-33-9%29%5E2%29 Plug in x%5B1%5D=23, x%5B2%5D=4, y%5B1%5D=-33, and y%5B2%5D=9.


d=sqrt%28%2819%29%5E2%2B%28-33-9%29%5E2%29 Subtract 4 from 23 to get 19.


d=sqrt%28%2819%29%5E2%2B%28-42%29%5E2%29 Subtract 9 from -33 to get -42.


d=sqrt%28361%2B%28-42%29%5E2%29 Square 19 to get 361.


d=sqrt%28361%2B1764%29 Square -42 to get 1764.


d=sqrt%282125%29 Add 361 to 1764 to get 2125.


d=5%2Asqrt%2885%29 Simplify the square root.


So our answer is d=5%2Asqrt%2885%29


Which approximates to d=46.098 (after using a calculator)


So the distance between the two points is approximately 46.098 units.