Question

Find the equation of the line through (2, 3) so that the segment of the line intercepted between the axes is bisected at this point.

Solution

Correct option is

3x + 2y = 12

 

Let the required line segment be AB

Let O be the origin and OA = a and OB = b.

 

Then the coordinates of A and B are (a, 0) and (0, b) respectively. 

.                       

   

Hence the equation of the required line is

             

i.e.,     3x + 2y = 12.

SIMILAR QUESTIONS

Q1

 

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

 

Q2

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).

Q3

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.

Q4

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

Q5

Find the equation to the straight line joining the points .

Q6

 

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.  

 

Q7

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

Q8

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

Q9

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).

Q10

 

Find the equation to the straight line which passes through the points (3, 4) and having intercepts on the axes: 

1. equal in magnitude but opposite in sign 

2. such that their sum is 14