Question

Find the orthocentre of the triangle whose sides are given by 4x-7y+10,x+y=5and7x+4y=15

Answer 1

Answer: A(1,2) is the orthocentre of triangle ABC

Step-by-step explanation:

Let the equation of the lines AB, BC and AC be 4x - 7y = - 10, x + y = 5 and 7x + 4y = 15 respectively.

A is the common point of lines AB and AC.

Solving equations of AB and AC, we get

A(1,2)

Now, the slope of AB = 4/7

And the slope of AC = - 7/4

So, the product of the slopes of AB and AC

= (4/7)*(- 7/4) = - 1

So, AB is perpendicular to AC

So, angle BAC is the right angle in triangle ABC

So, A(1,2) is the orthocentre of triangle ABC

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Hope this helps u....