Find the equation

Given: The vertices of ∆ABC are A (1, 4), B (− 3, 2) and C (− 5, − 3).

To find:

The equations of the altitudes of a ΔABC whose vertices are A (1, 4), B (-3, 2) and C (-5, -3).

Explanation:

Diagram:

Slope of AB

Slope of BC

Slope of CA

Thus, we have:

Slope of CF = -2

Slope of AD

Slope of BE

Hence,

Equation of CF is: y + 3 = -2(x + 5)

⇒ 2x + y + 13 = 0

Equation of AD is: y – 4(x – 1)

⇒ 2x + 5y – 22 = 0

Equation of BE is: y – 2(x + 3)

⇒ 6x + 7y + 4 = 0