Answer
Verified
91.2k+ views
Hint: - Centroid divides the line joining orthocenter and circumcenter in the ratio$2:1$
As we know the centroid divides the line joining orthocenter and circumcenter in the ratio$2:1$
Given orthocenter coordinates is $\left( {3, - 5} \right)$and centroid coordinates is$\left( {3,3} \right)$
Let the circumcenter be$\left( {x,y} \right)$
Then by section formula the coordinates of centroid is written as
$3 = \frac{{mx - 3n}}{{m + n}},{\text{ }}3 = \frac{{my - \left( { - 5} \right)n}}{{m + n}}$
Here$m = 2$and$n = 1$
\[
3 = \frac{{2x - 3}}{{2 + 1}},{\text{ }}3 = \frac{{2y + 5}}{{2 + 1}} \\
\Rightarrow 9 = 2x - 3,{\text{ }}9 = 2y + 5 \\
\Rightarrow x = \frac{{12}}{2} = 6 \\
\Rightarrow y = \frac{4}{2} = 2 \\
\]
Therefore the coordinates of circumcenter is$\left( {6,2} \right)$
Hence option c is correct.
Note: - In such types of question the key concept we have to remember is that the centroid divides the line joining orthocenter and circumcenter in the ratio$2:1$, then apply the section formula which is stated above, so after simplification we will get the required coordinates of the circumcenter.
As we know the centroid divides the line joining orthocenter and circumcenter in the ratio$2:1$
Given orthocenter coordinates is $\left( {3, - 5} \right)$and centroid coordinates is$\left( {3,3} \right)$
Let the circumcenter be$\left( {x,y} \right)$
Then by section formula the coordinates of centroid is written as
$3 = \frac{{mx - 3n}}{{m + n}},{\text{ }}3 = \frac{{my - \left( { - 5} \right)n}}{{m + n}}$
Here$m = 2$and$n = 1$
\[
3 = \frac{{2x - 3}}{{2 + 1}},{\text{ }}3 = \frac{{2y + 5}}{{2 + 1}} \\
\Rightarrow 9 = 2x - 3,{\text{ }}9 = 2y + 5 \\
\Rightarrow x = \frac{{12}}{2} = 6 \\
\Rightarrow y = \frac{4}{2} = 2 \\
\]
Therefore the coordinates of circumcenter is$\left( {6,2} \right)$
Hence option c is correct.
Note: - In such types of question the key concept we have to remember is that the centroid divides the line joining orthocenter and circumcenter in the ratio$2:1$, then apply the section formula which is stated above, so after simplification we will get the required coordinates of the circumcenter.
Recently Updated Pages
Name the scale on which the destructive energy of an class 11 physics JEE_Main
Write an article on the need and importance of sports class 10 english JEE_Main
Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main
Choose the one which best expresses the meaning of class 9 english JEE_Main
What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main
A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main
Other Pages
Derive an expression for maximum speed of a car on class 11 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main
3 mole of gas X and 2 moles of gas Y enters from the class 11 physics JEE_Main
The vapour pressure of pure A is 10 torr and at the class 12 chemistry JEE_Main
Electric field due to uniformly charged sphere class 12 physics JEE_Main
If the central portion of a convex lens is wrapped class 12 physics JEE_Main