Q. 44.3( 3 Votes )
Find the equations of the altitudes of a ΔABC whose vertices are A (1, 4), B(-3, 2) and C(-5, -3).
Answer :
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
Rate this question :
Various Forms of Equations of line45 mins
Parametric Equations of Straight line48 mins
Slope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of line23 mins
Straight line | Analyse your learning through quiz56 mins
General Equation of a line43 mins
Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 0372 mins
Motion in a Straight Line - 1169 mins
Find the equation of the line whose y - intercept is - 3 and which is perpendicular to the line joining the points ( - 2, 3) and (4, - 5).
RS Aggarwal - MathematicsFind the equation of the line which is perpendicular to the line 3x + 2y = 8 and passes through the midpoint of the line joining the points (6, 4) and (4, - 2).
RS Aggarwal - MathematicsFind the equation of the line passing through the point (2, 3) and perpendicular to the line 4x + 3y = 10
RS Aggarwal - MathematicsFind the equation of the line that has x - intercept - 3 and which is perpendicular to the line 3x + 5y = 4
RS Aggarwal - MathematicsFind the equation of a line that has y – intercept – 4 and is parallel to the line joining (2, – 5) and (1, 2).
RD Sharma - MathematicsFind the equation of the perpendicular to the line segment joining (4, 3) and (– 1 1) if it cuts off an intercept – 3 from y – axis.
RD Sharma - MathematicsIf equation of the line passing through (1, 5) and perpendicular to the line 3x – 5y + 7 = 0 is
RD Sharma - MathematicsFind the equation of the perpendicular drawn from the point P(-2, 3) to the line x– 4y + 7 = 0. Also, find the coordinates of the foot of the perpendicular.
RS Aggarwal - MathematicsFind the image of the point P(1, 2) in the line x – 3y + 4 = 0.
RS Aggarwal - Mathematics