Question

the distance between the point (0,0) and (a-b,a+b) is

Answer 1

The distance between the points (0, 0) and (a-b, a+b) is √(2a²+2b²)

Given:

The points (0, 0) and (a-b, a+b)  

To find:

The distance between given points

Solution:

Given points let O(0, 0) and A (a-b, a+b)

As we know

The distance between two points P(x, y) and Q(x₁, y₁)is given by  

                           PQ = √(x₁-x)²+(y₁-y²)  

The distance between O (0, 0) and X (a-b, a+b)

OA = $\sqrt{(a-b - 0)^{2} +(a+b - 0)^{2} }$

= $\sqrt{(a-b )^{2} +(a+b)^{2} }$

= $\sqrt{a^{2} +b^{2} -2ab +a^{2} +b^{2} +2ab}$

= $\sqrt{a^{2} +b^{2} +a^{2} +b^{2} }$

= $\sqrt{2a^{2} +2b^{2} }$

Therefore,

The distance between the points (0, 0) and (a-b, a+b) is √(2a²+2b²)

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