# Distance Formula

The distance formula is a fundamental concept in mathematics, particularly in geometry and analytic geometry. It provides a precise method for calculating the distance between two points in a coordinate plane. This formula, derived from the Pythagorean theorem, serves as a cornerstone for solving various problems related to spatial relationships and measurements. By applying the distance formula, mathematicians and scientists can determine the length of the shortest path between two points, whether in two-dimensional or three-dimensional space. Its simplicity and versatility make the distance formula an indispensable tool in fields ranging from physics and engineering to computer science and geography.

- Mike hiked to a lake in 3.5 hours at an average rate of #4 1/5# miles per hour. Pedro hiked the same distance at a rate of #4 3/5# miles per hour. How long did it take Pedro to reach the lake?
- What is the distance between (6,5) and (2,3)?
- What is the distance between (5,-3) and (0,9)?
- How do you find the distance between (–3, –2) and (1, 4)?
- What is the distance between # (-6, -6) # and # (4,0) #?
- What is the distance between #(-3,2)# and #(2,-2)#?
- What is the distance between #(-15,36)# and # (–3, 2) #?
- If #3a = 2.1# and #a+b=1.1#, what is the value of #b#?
- How do you find the value of a given the points (4,-1), (a,5) with a distance of #10#?
- How do you find a possible value for a if the points (a,-6), (-5,2) has a distance of #d=10#?
- What is the distance between #(5,-3)# and # (3,7) #?
- How do you find the distance between the points (0,2) and (3,0) on a graph?
- How do you find the possible values for a if the points (a,6), (-6,2) has a distance of #4sqrt10#?
- What is the distance between the points #(0, -2sqrt5)# and #(-sqrt6, 0)#?
- What is the distance between # (3, 2, 1) # and #(–1, 4, –2) #?
- What is the distance between #(2,-4)# and #(0,6)#?
- What is the distance between #(10,1,-4)# and #(-1,-1,3)#?
- What is the distance between # (–2, 1, 3) # and #(–1, 4, –2) #?
- How do you find the distance between points (-11, 9), (3,-4)?
- A tree grows #1 3/4# feet per year. How long will it take the tree to grow from a height of #21 1/4# feet to a height of 37 feet?