Q14 of 112 Page 166

If the vertices of a Δ ABC are A(2, –4), B(3, 3) and C(–1, 5). Find the equation of the straight line along the altitude from the vertex B.


Given: A ∆ABC has vertices A(2,–4),B(3,3) and C(–1,5).


The straight line BD drawn from vertex B is perpendicular to the line AC. So the product of the slopes of BD and AC is equal to –1.


Slope of AC is m1.



Where (x1,y1) and (x2,y2) are (2,–4) and (–1,5)


Therefore,


Slope of the BD is


=


Hence the equation of the line BD drawn from the vertex B is


(y–y1) = m(x–x1),here B is (3,3) and m =


⇒


⇒ 3(y–3) = (x–3)


⇒ 3y –9 = x–3


⇒ 3y–9–x + 3 = 0


⇒ –x + 3y–6 = 0


⇒ x–3y + 6 = 0


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