distance between two points

Question

what is the distance between (8,2) and (2,5)?

Answer 1

Hi Kinsey--

 

One way to solve this is to plot the 2 points and think of the line segment between them as the hypotenuse of a right triangle.

 

Then draw the 2 legs to complete the right triangle, and you can use the Pythagorean Theorem ( a² + b² = c²) to determine the length of the hypotenuse:

 

One possible plot point to complete the triangle is (2, 2), which makes the distance from there to (8,2) = 6, and the distance from (2,2) to (2,5) = 3

 

So 3 squared + 6 squared = ? squared

 

9 + 36 = 45, so the hypotenuse's length is the square root of 45.

 

Hope this helps!

 

Matt in New York

Answer 2

Given any two points in the Cartesian coordinate plane (X₁,X₁) and (Y_2,Y₂), their distance can be calculated using the formula S = √(X₂—X₁)² + (Y₂ —Y₁)² . Therefore,  S = √(8 — 2)² + (2 —5)² = 3√5

 

Answer 3

Use distance formula.

 

d = √(x₂ - x₁)² + (y₂ - y₁)²    Given (8,2) (2,5)

 

d = √(2-8)² + (5-2)²

 

d = √(36 + 9) ⇒ √45

 

d = 3√5