Q. 134.3( 6 Votes )

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

Answer :

Given: coordinates of the orthocenter of the triangle whose vertices are ( - 1, 3), (2, - 1) and (0, 0).


Assuming:


A (0, 0), B (−1, 3) and C (2, −1) be the vertices of the triangle ABC.


Let AD and BE be the altitudes.


To find:


Orthocenter of the triangle.


Explanation:



ADBC and BEAC


The slope of AD × Slope of BC = −1


The slope of BE × Slope of AC = −1


Here, the slope of BC =


and slope of AC =


slope of AD × ( - 4/3) = - 1 and slope of BE × ( - 1/2) = - 1


slope of AD and slope of BE = 2


The equation of the altitude AD passing through A (0, 0) and having slope is


y - 0 ( x - 0)


y x …..(1)


The equation of the altitude BE passing through B (−1, 3) and having slope 2 is


y - 3 = 2(x + 1)


2x – y + 5 = 0 …….(2)


Solving (1) and (2):


x = − 4, y = − 3


Hence, the coordinates of the orthocentre is (−4, −3).


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