Find The Coordinates Of The Orthcentre Of The Triangle Whose Vertices Are (0, 0), (2, –1) And (–1, 3).

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Question

Find the coordinates of the orthcentre of the triangle whose vertices are (0, 0), (2, –1) and (–1, 3).

Solution

Correct option is

(–4, –3).

   

                           

Since AL ⊥ BC, therefore equation of line AL is

                            

  

Slope of AC = –3   

Since BM ⊥ AC, therefore, equation of line BM is  

                   

or              x – 3y = 5                                                    …(ii)

Solving equations (i) and (ii), we get x = – 4, y = –3

∴ Orthocentre (–4, –3).

Testing

SIMILAR QUESTIONS

Q1

The line x + λy – 4 = 0 passes through the point of intersection of 4x – y+ 1 = 0 and x + y + 1 = 0. Find the values of λ.

Q2

Find the equation of a line parallel to x + 2y = 3 and passing through the point (3, 4).

Q3

Find the equation of the line perpendicular to 2x – 3y = 5 and cutting off an intercept 1 on the x-axis

Q4

Find the equation of the straight line passing through (2, –9) and the point of intersection of lines 2x + 5y – 8 = 0,

3x – 4y – 35 = 0  

Q5

Find the equation of straight line passing through the point of intersection of lines 3x – 4y +1 = 0, 5x + y – 1 = 0 and cutting off equal intercepts from coordinate axes.

Q6

Find the distance between the lines 5x + 12y + 40 = 0 and 10x + 24y – 25 = 0.

 

Q7

If P is (1, 2) and the line mirror is 2x – y + 4 = 0, find the coordinates of its image (i.e., Q).

Q8

Find the values of λ for which the point (2 – λ, 1 + 2λ) lies on the non-origin side of the line 4x – y – 2 = 0. 

Q9

Find the incentre of ΔABC if A is (4, –2), B is (–2, 4) and C is (5, 5).

Q10

Find straight lines represented by 6x2 + 13xy + 6y2 + 8x + 7y + 2 = 0 and also find the point of intersection.