Home
Class 12
MATHS
The othocenter of DeltaABC with vertices...

The othocenter of `DeltaABC` with vertices `B(1,-2)` and `C(-2,0)` is `H(3,-1)`.Find the vertex A.

Text Solution

Verified by Experts

The correct Answer is:
`(3//7,-34//7)`
Let the coordinates of vertex A be (x,y).
`AHbotBC`
or `("Slope of" AH)xx("Slope of" BC) =1`
or `(y+1)/(x-3)xx(-2-0)/(1-(-2)=-1`
or `3x-2y=11`
Also, `BHbotAC`
or `("Slope of" BH)xx("Slope of" AC)=1`
or `(-2-(-1))/(1-3)xx(y-0)/(x-(-2))=-1`
or `-y=2x+4`
or `2x+y=-4`
Solving (1) and (2) , we get
`x=(3)/(7),y=-(34)/(7)`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Concept applications 1.5|5 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Concept applications 1.6|9 Videos

  • COORDINATE SYSYEM

    CENGAGE PUBLICATION|Exercise Concept applications 1.3|10 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

Find the orthocentre of Delta A B C with vertices A(1,0),B(-2,1), and C(5,2)

The incenter of the triangle with vertices (1,sqrt(3)),(0,0), and (2,0) is (a) (1,(sqrt(3))/2) (b) (2/3,1/(sqrt(3))) (c) (2/3,(sqrt(3))/2) (d) (1,1/(sqrt(3)))

Find the area of the tirangle with vertices A (1,1,2),B (2,3,5) and C(1,5,5).

The vertices A,B and C of DeltaABC have coordinates (-3,-2),(2,-2) and (6,1) respectively . Find the area of the DeltaABC and the length of the perpendicular from A on overline(BC) .

Find the area of triangle whose vertices are :A(1,-1),B(-2,0),C(0,-4)

B and C are the vertex of a triangle ABC with coordinate (2 , 0) and (8 , 0) respectively. Another vertex A moves in such a way that it satisfies the relation 4 " tan" (B)/(2) "tan" (C)/(2) = 1 . If the equation of locus of A is (x - 5)^(2)/5^2+ (y^(2))/(k^(2)) = 1 , then the value fo k is _

Consider a triangle with vertices A(1,2),B(3,1), and C(-3,0)dot Find the equation of altitude through vertex A the equation of median through vertex A the equation of internal angle bisector of /_A

In the triangle ABC with vertices A (2, 3) , B (4, -1) " and " C (1, 2) , find the equation and length of altitude from the vertex A.

The coordinates of two vertices of a triangle are (-2,3) and (5,-1) . If the orthocentre of the triangle is at the origin , find the coordinates of its third vertex.

Find the co-ordinate of the orthocentre of a triangle whose vertices are A(-2,-3),B(6,1)and C(1,6).