Question

Find the equations of the medians of a triangle, the coordinates of whose vertices are (–1, 6), (–3, –9) and (5, –8).

Solution

Correct option is

 

29x + 4y + 5 = 0, 8x – 5y – 21 = 0, 13x + 14y + 47 = 0

 

Let A(–1, 6), B(–3, –9) and C(5, –8) be the vertices of ∆ABC. Let DEand F be the mid-points of the sides BCCA and AB respectively.                                                 

  

  

i.e.,       (2, –1) 

  

i.e.,       (–2, –3/2)  

∴ Equation of the median AD = Equation of line through (–1, 6) and  is 

       

   

or    29x + 4y + 5 = 0 

Equation of median BE is  

       

i.e.,  8x – 5y – 21 = 0 

and equation of median CF is  

        

i.e.   13x + 14y + 47 = 0

SIMILAR QUESTIONS

Q1

Find the equation of the straight line cutting off an intercept of 3 units on negative direction of y-axis and inclined at an angle  to the axis of x.

Q2

Find the equation to the straight line cutting off an intercept of 5 units on negative direction of y-axis and being equally inclined to the axes.  

Q3

 

Find the equations of the bisectors of the angle between the coordinate axes.

 

Q4

Find the equation of a line which makes an angle of 135o with positive direction of x-axis and passes through the point (3, 5).

Q5

Find the equation of the straight line bisecting the segment joining the points (5, 3) and (4, 4) and making an angle of 45o with the positive direction of x-axis.

Q6

Find the equation of the right bisector of the line joining (1, 1) and (3, 5).

Q7

Find the equation to the straight line joining the points .

Q8

 

Let ABC be a triangle with A(–1, –5), B(0, 0) and C(2, 2) and let D be the middle point of BC. Find the equation of the perpendicular drawn from Bto AD.  

 

Q9

The vertices of a triangle are A(10, 4), B(–4, 9) and C(–2, –1). Find the equation of the altitude through A.

Q10

Find the ratio in which the line segment joining the points (2, 3) and (4, 5) is divided by the line joining (6, 8) and (–3, –2).