## 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

3*x* + 2*y* = 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., 3*x* + 2*y* = 12.

#### SIMILAR QUESTIONS

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

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

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

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

Find the equation to the straight line joining the points .

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 *B*to *AD*.

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

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

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).

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