## Question

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.

### Solution

*x* – *y* – 1 = 0

Here, *m* = slope of the line = tan 45^{o} = 1.

Let *A* be the mid-point of (5, 3) and (4, 4). Then the coordinates of *A* are

Hence the required equation of the line is

or *x* – *y* – 1 = 0

#### SIMILAR QUESTIONS

Find the equation of the straight line parallel to *x*-axis and at a distance

(i). 5 units above the *x*-axis

(ii). 9 units below the *x*-axis

Find the equation of the straight line which passes through the point (2, –3) and is

1. parallel to the x-axis

2. perpendicular to the x-axis

Find the equation of a line which is equidistant from the lines .

If the straight line *y* = *mx* + *c* passes through the points (2, 4) and (–3, 6), find the values of *m* and *c*.

What are the inclination to the x-axis and intercept on y-axis of the line

?

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*.

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.

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