Answer
424.5k+ views
Hint: First, before proceeding for this, we must draw the triangle in the graph so that we get to know what this triangle looks like. Then, we should be aware of the fact that in a right angled triangle, the value of the circumcentre of the triangle is the midpoint of the hypotenuse. Then, by using midpoint formula for the points $ \left( {{x}_{1}},{{y}_{1}} \right) $ and $ \left( {{x}_{2}},{{y}_{2}} \right) $ as $ x=\dfrac{{{x}_{1}}+{{x}_{2}}}{2},y=\dfrac{{{y}_{1}}+{{y}_{2}}}{2} $ , we get the desired answer.
Complete step-by-step answer:
In this question, we are supposed to find the circumcentre of the triangle with vertices (0, 0), (3, 0) and (0, 4).
So, before proceeding for this, we must draw the triangle in the graph so that we get to know what this triangle looks like.
So, we can clearly see from the figure that the graph of the triangle with vertices (0, 0), (3, 0) and (0, 4) is a right angled triangle.
Now, we should be aware of the fact that in a right angled triangle, the value of the circumcentre of the triangle is the midpoint of the hypotenuse.
Now, we need to use the midpoint formula to calculate the circumcentre of the given triangle.
So, midpoint formula for the points $ \left( {{x}_{1}},{{y}_{1}} \right) $ and $ \left( {{x}_{2}},{{y}_{2}} \right) $ are given by:
$ x=\dfrac{{{x}_{1}}+{{x}_{2}}}{2},y=\dfrac{{{y}_{1}}+{{y}_{2}}}{2} $
So, now the points $ \left( {{x}_{1}},{{y}_{1}} \right) $ from the figure is (3, 0) and points $ \left( {{x}_{2}},{{y}_{2}} \right) $ is (0, 4).
Then, by using the values of the above points, we get the coordinates of the midpoint of hypotenuse of the triangle as:
$ x=\dfrac{3+0}{2},y=\dfrac{0+4}{2} $
Then, solve the above expression to get the value of coordinates as:
$ \begin{align}
& x=\dfrac{3}{2},y=\dfrac{4}{2} \\
& \Rightarrow x=\dfrac{3}{2},y=2 \\
\end{align} $
So, the values of the midpoints of the hypotenuse is $ \left( \dfrac{3}{2},2 \right) $ which is also the value of circumcentre of the right angled triangle with vertices as (0, 0), (3, 0) and (0, 4).
So, the correct answer is “Option C”.
Note: Now, to solve these types of questions we need to be careful with the coordinates as the first coordinate is always x coordinate and second coordinate is always y-coordinate. If we confuse between them and select y as first coordinate then we get our answer as option (b) which is a wrong answer. So, we must be careful about the coordinate system.
Complete step-by-step answer:
In this question, we are supposed to find the circumcentre of the triangle with vertices (0, 0), (3, 0) and (0, 4).
So, before proceeding for this, we must draw the triangle in the graph so that we get to know what this triangle looks like.
![seo images](https://www.vedantu.com/question-sets/b1909c82-ead0-450e-8f09-f1d2126cbfdf316372181326777098.png)
So, we can clearly see from the figure that the graph of the triangle with vertices (0, 0), (3, 0) and (0, 4) is a right angled triangle.
Now, we should be aware of the fact that in a right angled triangle, the value of the circumcentre of the triangle is the midpoint of the hypotenuse.
Now, we need to use the midpoint formula to calculate the circumcentre of the given triangle.
So, midpoint formula for the points $ \left( {{x}_{1}},{{y}_{1}} \right) $ and $ \left( {{x}_{2}},{{y}_{2}} \right) $ are given by:
$ x=\dfrac{{{x}_{1}}+{{x}_{2}}}{2},y=\dfrac{{{y}_{1}}+{{y}_{2}}}{2} $
So, now the points $ \left( {{x}_{1}},{{y}_{1}} \right) $ from the figure is (3, 0) and points $ \left( {{x}_{2}},{{y}_{2}} \right) $ is (0, 4).
Then, by using the values of the above points, we get the coordinates of the midpoint of hypotenuse of the triangle as:
$ x=\dfrac{3+0}{2},y=\dfrac{0+4}{2} $
Then, solve the above expression to get the value of coordinates as:
$ \begin{align}
& x=\dfrac{3}{2},y=\dfrac{4}{2} \\
& \Rightarrow x=\dfrac{3}{2},y=2 \\
\end{align} $
So, the values of the midpoints of the hypotenuse is $ \left( \dfrac{3}{2},2 \right) $ which is also the value of circumcentre of the right angled triangle with vertices as (0, 0), (3, 0) and (0, 4).
So, the correct answer is “Option C”.
Note: Now, to solve these types of questions we need to be careful with the coordinates as the first coordinate is always x coordinate and second coordinate is always y-coordinate. If we confuse between them and select y as first coordinate then we get our answer as option (b) which is a wrong answer. So, we must be careful about the coordinate system.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)