Step-by-step explanation:
Given - The distance between point (2, 2) and point (8, 2) is 6 units on
a coordinate plane.
To find - Which other pairs of points are also 6 units apart?
Proof -
The distance between two points (x₁, y₁), (x₂, y₂) are 6 if and only if either
( x₂ - x₁ = 6 and y₂ = y₁ )or ( x₂ = x₁ and y₂ - y₁ = 6 ).
If either of the conditions is satisfied , then only we can say that the two points has ha distance of 6 units between them.
Now, As given
Let (x₁, y₁) = ( 2, 2) , (x₂, y₂) = (8, 2)
Check whether the conditions are satisfied or not .
Here x₁ = 2 , x₂ = 8, y₁ = 2, y₂ = 2
Now,
x₂ - x₁ = 8 - 2 = 6 , y₂ - y₁ = 2 - 2 = 0
∴ we get
1st condition is satisfied, So the points have a distance of 6 units between them.
Now,
Let us suppose another point (x₁, y₁) = ( 4, 3) , (x₂, y₂) = (3, 3)
Here x₁ = 4 , x₂ = 3, y₁ = 3, y₂ = 3
Now,
x₂ - x₁ = 4 - 3 = 1 , y₂ - y₁ = 3 - 3 = 0
Here neither of the conditions are satisfied.
So the points are not at a distance of 6 units from each other.
