# Find the co-ordinates of the orthocentre of triangle ABC whose vertices are A(1,2), B(2,3) and C(4,3)

Slope of AB=$\frac{3-2}{2-1}=1$

Slope of BC=$\frac{3-3}{4-2}=0$

Slope of CA=$\frac{3-2}{4-1}=\frac{1}{3}$

Let AD, BE and CF be the altitudes in $△ABC$

Then,

Slope of BE=

Slope of CF=

We now have the vertices and slopes of AD, BE and CF. Let (x, y) be the orthocentre. So, by the equation $y-{y}_{1}=m\left(x-{x}_{1}\right)$, we have:-

Solving these equations, we find x=1, y=6

Thus, the required orthocentre is (1, 6).

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