Question

Find the orthocenter of triangle formed by the points(-5, -7), (13, 2), (-5,6) ?

Answer 1

Answer:

(-4,-3)

Step-by-step explanation:

Slope of AC =m=

−1−0

3−0

=−3

Draw BD perpendicular to AC and its slope be m

′

mm

′

=−1

−3m

′

=−1

⇒m

′

=

3

1

Equation of BD is

y+1=

3

1

(x−2)

3y+3=x−2

x−3y=5.........(i)

Now slope of AB =m

AB

=

2−0

−1−0

=−

2

1

Draw CE perpemdicular AB

=m

AB

=

2−0

−1−0

=−

2

1

m

AB

m

CE

=−1

−

2

1

m

CE

=−1

⇒m

CE

=2

Equation of CE is

y−3=2(x+1)

2x−y+5=0......(ii)

Orthocentre is the point of intersection of perpendiculars drawn from opposite vertices . So it is the point of intersection of BD and CE

Solving (i) and (ii) by substituting x from (i) in (ii)

y−3=2(x+1)

2(3y+5)−y+5=0

6y+10−y+5=0

5y+15=0

⇒y=−3

x=3(−3)+5

⇒x=−4

So the orthocentre of the triangle is (−4,−3)