If a ABC has vertices A(-1,7), B(-7,1) and C(5,-5), then its orthocentre has coordinates:

Question

If a $	riangle ABC$ has vertices $A(-1,7),\ B(-7,1)$ and $C(5,-5)$, then its orthocentre has coordinates:

Accepted Answer

Slope of $BC = \dfrac{-5-1}{5+7}=-\dfrac12$; altitude from $A$ perpendicular to $BC$ has slope $2$: $y-7=2(x+1) \implies y=2x+9$ \ldots  (i)

Slope of $AC = \dfrac{-5-7}{5+1}=-2$; altitude from $B$ perpendicular to $AC$ has slope $\dfrac12$: $y-1=\dfrac12(x+7) \implies y=\dfrac x2+\dfrac92$ \ldots  (ii)

Solving (i),(ii): $2x+9=\dfrac{x+9}2 \implies 4x+18=x+9 \implies 3x=-9\implies x=-3,\ y=3$

$$\text{Orthocentre} = (-3,3)$$

Solutions · 1