Question

the distance between the points 0,0 and (a-b, a+b) is
Options
(A). 2√ab
(B). √2a^2+ab
(C). 2√a^2+b^2
(D). √2a^2+2b^2

Answer 1

Answer:

Step-by-step explanation:

OPTION [C]

Answer 2

The correct answer is option (D)√(2a²+2b²)

Given:

Points (0,0) and (a-b, a+b) is

To find:

The distance between the given points

Solution:

Let given points are O(0,0) and A(a-b, a+b) is

The distance between a point P(x, y) from the origin is given by

                          OP = √(x²+y²)  

Therefore, distance between the points O(0,0) and A(a-b, a+b) is

OA = $\sqrt{(a-b)^{2} +(a+b)^{2} }$  

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

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

= $\sqrt{2a^{2} +2 b^{2} }$  

Therefore,

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

The correct answer is option (D)√(2a²+2b²)

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