Question

The orthocentre of the triangle formed by (0,0), (8,0) and (4,6) is

Answer 1

(10/9,19/6) it is the coordinates of orthocentre

Answer 2

Answer:

Consider a triangle ABC with coordinates A(0,0), B(4,6) and C (8,0) respectively.

From point A make a line AD perpendicular to BC and from point C make a line CE perpendicular to AB. Mark their point of intersection as O(orthocentre).

Now,

mBC =0-6/8-4=-3/4

mBC ×mAD=-1

mAD=-1/mBC

mAD=2/3

By two point formula

y-0=2/3(x-0)

y=2x/3...........(1)

mAB=6-0/4-0

mAB=3/2

mAB×mCE=-1

mCE=-1/mAB

mCE=-2/3

By two point formula

y-0=-2/3(x-8)

y=-2x/3 +16/3

Put value of y from equation (1)

2x/3=-2x/3+16/3

x=4

Putting value of x in equation (1),we get

y=2(4)/3

y=8/3

So the coordinates of orthocentre are O(4,8/3)