find the distance d[p1,p2]

Question

p1=[-3,2]

p2=[5,6]

 

Answer 1

Recall the Pythagorean theorem:

a² + b² = c²

Where a and b are the legs of a right triangle and c is the hypotenuse. (This is one of the most important formulas in all of mathematics)

This formulas can be rearranged as follows:

c = √(a² + b²)

The formula can be applied to this problem by making "a" the difference in the x values of the points (x₂-x₁) and the "b" the difference of the y values (y₂- y₁). (Do you see how these are the legs of a right triangle?) The "c" value is then the distance between them (the hypotenuse).

The common mistakes are not squaring the "a" and "b" or more commonly not taking the square root as the final step.

Be sure to check your final result: it must be greater than or equal to either of the legs. t also cannot be greater than the sum of the legs.

Answer 2

So the distance between 2 points P₁, P₂ where P₁ = (x₁, y₁), and P₂ = (x₂, y₂) can be defined as:

d = sqrt[(y₂ - y₁)^2 + (x₂ - x₁)^2].

So for your points P₁ = (-3, 2), and P₂ = (5, 6), we can find the distance between those 2 points by substituting our given values into the equation above.

We get:

d = sqrt[(6 - 2)^2 + (5 - (-3))^2]

which simplifies to:

d = sqrt[(4)^2 + (8)^2] = sqrt[16 + 64]) = sqrt(80) = 4*sqrt(5)

So the distance between those two points is 4*sqrt(5)