## Question

Find the measure of the angle of intersection of the lines whose equations are 3*x* + 4*y* + 7 = 0 and 4*x* – 3*y* + 5 = 0.

### Solution

0

Given lines are 3*x* + 4*y* + 7 = 0, 4*x* – 3*y* + 5 = 0

Comparing the given lines with *A*_{1}*x* + *B*_{1}*y* + *C*_{1} = 0,

*A*_{2}*x* + *B*_{2}*y* + *C*_{2} = 0 respectively, we get

*A*_{1} = 3, *B*_{1} = 4 and *A*_{2} = 4, *B*_{2} = –3

Hence the given lines are perpendicular.

#### SIMILAR QUESTIONS

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

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

Find the equation of the straight line through the point *P*(*a*, *b*) parallel to the lines . Also find the intercepts made by it on the axes.

The length of perpendicular from the origin to a line is 9 and the line makes an angle of 120^{o} with the positive direction of y-axis. Find the equation of the line.

Find the equation of the straight line on which the perpendicular from origin makes an angle of 30^{o} with x-axis and which forms a triangle of area sq. units with the coordinates axes.

Find the angle between the lines

where *a* > *b* > 0.