Question

① The vertices of a triangle ABCare
A (3,4) B (√12, √13) C (-1, 2√6
The orthocentre of the triangle
ABC​

Answer 1

Answer:

Orthocenter is point of intersection of altitudes

m

AD

⋅m

BC

=−1

m

BC

=

1−2

3+1

=−4

⇒m

AD

=

4

1

∴ Equation of AD is y=

4

1

x

m

BE

⋅m

AC

=−1, m

AC

=

1

3

⇒m

BE

=

3

−1

Equation of BE is

3

−1

(x−2)=(y+1)

⇒−x+2=3y+3

⇒x+3y+1=0

Point of intersection of AD & BE is 'H'(orthocentre)

⇒y=

4

x

& x+3y+1=0, ⇒x=4y

4y+3y+1=0 ⇒y=

7

−1

⇒x=

7

−4

Orthocentre(

7

−4

,

7

−1

).

Step-by-step explanation:

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