Find the co-ordinates of the orthocenter of the triangle whose vertices are A(3,−2), B(7,6), C(−1,2).

5.4 · Q71

Q. Find the co-ordinates of the orthocenter of the triangle whose vertices are A(3,-2), B(7,6), C(-1,2).

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Vertices $A(3,-2)$ , $B(7,6)$ , $C(-1,2)$ . Altitude from $A\perp BC$ : slope $BC=\dfrac{2-6}{-1-7}=\dfrac12$ , altitude slope $=-2$ : $y+2=-2(x-3) \Rightarrow 2x+y-4=0$ ...(i). Altitude from $B\perp AC$ : slope $AC=\dfrac{2+2}{-1-3}=-1$ , altitude slope $=1$ : $y-6=x-7 \Rightarrow x-y-1=0$ ...(ii). From (ii), $y …

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Q.Find the co-ordinates of the orthocenter of the triangle whose vertices are A(3,−2), B(7,6), C(−1,2).

Concept understanding — Slope of a Line

Q.Find the co-ordinates of the orthocenter of the triangle whose vertices are A(3,−2), B(7,6), C(−1,2).

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