Question

O(0, 0), A(1, 2), B(3, 4) are the vertices of Triangle OAB. The joint equation of the altitude and median drawn from O is ​

Answer 1

Answer:

OD is the median

∴ D = (1+32,2+42)

⇒ D = (2, 3)

Equation of OD is y = mx

⇒ y =

32x ⇒ 3x - 2y = 0

Slope of line AB =

22=1

Given, OE ⊥ AB

∴ Slope of OE= -1

Equation of OE is y = mx

⇒ y = -x ⇒ x + y = 0

∴ Joint equation of median and altitude is

(3x - 2y) (x + y) = 0

⇒ 3x2 + xy - 2y2 = 0