Given triangle ABC with vertices A(−3, 0), B(0, 6), and C(4, 6). c Find the equations of the three altitudes of the same triangle
Answers
Given info : Given triangle ABC with vertices A(−3, 0), B(0, 6), and C(4, 6).
To find : the equations of the three altitudes of the same triangle.
Solution : let AM, BN and CL are the altitudes on BC , CA and AB respectively.
equation of altitude AM :
slope of AM = -1/slope of BC [ because altitude is perpendicular on line BC]
= -1/(6 - 6)/(4 - 0) = ∞
Now equation of AM , (y - 0) = ∞(x + 3)
⇒y = 1/0 (x + 3)
⇒x + 3 = 0
Equation of altitude BN :
Slope of BN = -1/slope of CA
= -1/(6 - 0)/(4 + 3) = -7/6
Now equation of BN, (y - 6) = -7/6(x - 0)
⇒6(y - 6) + 7x = 0
⇒7x + 6y - 36 = 0
equation of altitude CL :
slope of CL = -1/slope of AB
= -1/(6 - 0)/(0 + 3) = -3/6 = -1/2
equation of CL , (y - 6) = -1/2(x - 4)
⇒2(y - 6) + (x - 4) = 0
⇒2y - 12 + x - 4 = 0
⇒x + 2y - 16 = 0