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