Question

28. If(a, b), (x, y), (p,q) are the coordinates ofcircumcentre, centroid, orthocentre of thereetriangle then1) 3x = 2a + p, 3y = 2b+q2) x = 3a + 2p, y=3b+ 2q3) 3x = a + 2p, 3y=b+ 2q4) x = a +p, y=b+q​

Answer 1

Step-by-step explanation:

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(α,β) and G(

x

ˉ

,

y

ˉ

)

Then by the section formula:

⟹

y

ˉ

=

3

2β+q

⟹3

y

ˉ

=2β+q and

⟹

x

ˉ

=

3

2α+p

⟹3

x

ˉ

=2α+p