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|Exercise Exercise 1.5|5 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.6|9 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.3|10 Videos

  • COORDINATE SYSTEM

    CENGAGE|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE|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 triangle with vertices A(1,1,2)B(2,3,5) and C(1,5,5).

Consider the triangle ABC with vertices A(1,2,3) , B(-1, 0, 4) and C(0, 1, 2) (a) Find vec (AB) and vec (AC) Find angle A . (c) Find the area of triangle ABC.

If the centroid of a triangle is at (10,-1) and two vertices are (3,2) and (5,-11). Find the third vertex of a triangle .

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.

Find the area of triangle ABC given that vertices are A(2,1,-2) B(1,4,2) and C(3,-1,-1).

The area of the triangle whose vertices are A(1,-1,2),B(2,1-1)C(3,-1,2) is …….

The area of a triangle is 5. Two of its vertices are A(2,1) and B(3,-2) . The third vertex C is on y=x+3. Find Cdot