CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If $$(\alpha \, , \, \beta) \, , \, (\bar{x} \, , \,\bar{y})$$ and (p , q) are the co - ordinates of the circumcentre, centroid and orthocentre of a triangle, then $$3\bar{x} \, = \,2\alpha +p \, \, \, and \, \, \, 3\bar{y} \, = \, 2\beta \, + \, q$$


A
True
loader
B
False
loader

Solution

The correct option is A True

 

Let, 

H,OandG be the orthocentre, circumcentre and centroid

of any triangle.

Then, these points are collinear.

Further, G divides the line segment HO from H in the ratio $$2:1$$

Here,

$$H(p,q), O(\alpha, \beta)$$ and $$G(\bar x, \bar y)$$

Then by the section formula:

$$\implies \bar y=\dfrac{2\beta +q}{3}\implies3\bar y=2\beta+q$$ and 

$$\implies \bar x=\dfrac{2\alpha+p}{3}\implies 3\bar x=2\alpha +p$$

 


Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More



footer-image