## Question

Show that the lines 2*x* – *y* – 12 = 0 and 3*x* + *y* – 8 = 0 intersect at a points which is equidistant from both the coordinates areas.

### Solution

(4, –4)

2*x* – *y* – 12 = 0

3*x* + *y* – 8 = 0

Using cross multiplication rule, we have

So, the point is (4, –4) which is at a distance 4 units from both the coordinate axes.

#### SIMILAR QUESTIONS

A straight line segment of length *‘p’* moves with its ends on two mutually perpendicular lines. find the locus of the point which divides the line in the ratio 1:2.

Find the acute angle between the two lines with slopes 1/5 and 3/2.

If a line has a slope = ½ and passes through (–1, 2); find its equation.

If a line has a slope 1/2 and cuts off along the positive *y*-axis of length 5/2 find the equation of the line.

If a line passes through two points (1, 5) and (3, 7) find its equation.

A straight line passes through a point A (1, 2) and makes an angle 60^{o}with the *x*-axis. This line intersects the line *x* + *y* = 6 at the point *P*. find *AP*.

Find the equation of the straight line, which passes through the point (3, 4) and whose intercept on *y*-axis is twice that on *x*-axis.

Find the equation of the straight line upon which the length of perpendicular from origin is units and this perpendicular makes an angle of 75^{o} with the positive direction of *x*-axis.

Find the value of *k* so that the straight line 2*x* + 3*y* + 4 + *k* (6*x* – *y* + 12) = 0 and 7*x* + 5*y* – 4 = 0 are perpendicular to each other.

Find the area of triangle formed by the lines *x* – *y* + 1 = 0, 2*x* + *y* + 4 = 0 and *x* + 3 = 0.