Question

Find the distance between the points P(a+b,a-b) and Q(a-b,-a-b)

Answer 1

Answer:

2√(a² + b²)

Step-by-step explanation:

Distance between two points = √(x₂ - x₁)² + (y₂ - y₁)²

P(a+b, a-b), Q(a-b, -a-b)

Distance between two points PQ = √(a-b-a-b)² + (-a-b -a + b)²

                                                         = √4b² +4a²

                                                          = 2√(a² + b²)

Answer 2

PQ^2= [a+b-(a-b)]^2 + [a-b-(-a-b)]^2

=2b*2b+2a*2a

=4b^2+4a^2

=4(a^2+b^2)