Find the distance between....

Question

Find the distance between the pair of points

 

(x+y,x) and (x-y,y)

Answer 1

Hello Kelly, 

All you have to do is use the distance formula

(x+y, x) becomes (x1, y1) and

(x-y,y) becomes (x2,y2)

 

The distance formula is 

sq. root of [(x2-x1)^2 + (y2-y1)^2]     Substituting

sq. root of [(x-y-x-y)^2+ (y-x)^2].      (x-y)-(x+y)=-2y

sq. root of [ (-2y)^2 + (y-x)(y-x)]        Using the foil method

sq. root of [ 4y^2+ ( y^2-2xy+x^2]    Combining like terms

sq. root of [ 5y^2-2xy+x^2]= distance

 

I hope this helps out. 

D.Y. Taylor

Answer 2

The distance between two points (x₁, y₁) and (x₂, y₂) can be found with the equation

d = √[(x₂-x₁)² + (y₂-y₁)²]

 

For your problem,

x₁ = x+y

y₁ = x

x₂ = x-y

y₂ = y

 

So,

d = √[((x-y) - (x+y))² + (y-x)²]

d = √[(-2y)² + (y-x)²]

 

Simplify what's on the inside, foil out the second term, and combine like terms. The answer is a quadratic in x and y under the square root.