Question

X(4,9), Y(-5,4) and Z(7,-4) are the vertices of a triangle. Find the equation of the altitude of the triangle through X.

Answer 1

The altitude through X is perpendicular tp YZ.

         Slope of YZ = `(-4 - 4)/(7 + 5) = (-2)/3`

⇒ m = Slope of YZ = `(-2)/3`

Slope line perpendicular to YZ will be `(-1)/"m" = 3/2`

This line passes through X(4,9)

Using the point slope Formulae,

y - y₁ = m(x - x₁)

y - 9 = `3/2`(x - 4)

⇒ 2y - 18 = 3x - 12

⇒ 2y = 3x + 6