Answer

Verified

428.4k+ views

**Hint**: Write the coordinate on the Cartesian plane and give them some name. Form a right angle triangle by joining those points with the origin. Then find all the sides of the triangle using distance formula. And then substitute them in the Pythagoras theorem to solve the question.

**:**

__Complete step-by-step answer__Observe the diagram

According to the question, $ (a,b),(c,d) $ subtend a right angle at the origin.

Now, observe the diagram and let us assume that A and B are the points which have the coordinates $ (c,d) $ and $ (a,b) $ respectively.

Then using distance formula, we can write

$ O{B^2} = {a^2} + {b^2} $

$ O{A^2} = {c^2} + {d^2} $

$ A{B^2} = {(a - c)^2} + {(b - d)^2} $

And by using Pythagoras theorem, we can write

$ A{B^2} = O{A^2} + O{B^2} $

By substituting the value of in the above equation, we get

$ {(a - c)^2} + {(b - d)^2} = {c^2} + {d^2} + {a^2} + {b^2} $

Now, by using the expansion formula of square, $ {(a - b)^2} = {a^2} + {b^2} - 2ab $ , we can expand the above equation as,

$ {a^2} + {c^2} - 2ac + {b^2} + {d^2} - 2bd = {c^2} + {d^2} + {a^2} + {b^2} $

By cancelling the common terms, we get

$ - 2ac - 2bd = 0 $

By taking common terms out, we get

$ - 2(ac + bd) = 0 $

$ \Rightarrow ac + bd = 0 $

Therefore, from the above explanation, the correct answer is, option (B) $ ac + bd = 0 $

**So, the correct answer is “Option B”.**

**Note**: Always draw a rough diagram. It helps to understand what approach should be taken to solve the question. Like in this question, it became easy to observe in the diagram that we can use the Pythagoras theorem as well as distance formula and then compare the two to find the answer.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How do you graph the function fx 4x class 9 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Change the following sentences into negative and interrogative class 10 english CBSE