A line passes through P(1, 2) such that its intercept between the axes is bisected at P. Find the equation of line.

Using slopes, show that the points A(-4,-1), B(-2,-4), C(4,0) and D(2,3) taken in order, are the vertices of a rectangle.

Find the equation of a line with slope -4 and cutting off an intercept of 4 units on negative direction of y-axis.

Find the length of the perpendicular from the point (2, -5) to the line joining the points (1, 4) and (3, 8).

Find the new coordinates of point (3,-4), if the origin is shifted to (1,2) by a translation.

Find the slope of a line joining following two points
(3,-2) and (7,-2)

Find the coordinates of the foot of the perpendicular from the point(2,3)on the line x+y-11=0

Find the equation of line passing through the points(-1,1) and (2,-4)

If three points (h,0), (a,b) and (0,k) lie on a line, show that \(\frac { a }{ h } +\frac { b }{ k } =1.\)

Show that the points A(7,10),B(-2,5) and C(3,-4) are the vertices of an isosceles right angled triangle.

Which of the lines 2x - y + 3 = 0 and ax - 4y - 7 = 0, is farther from the origin?

Find the equation of two straight lines which are parallel to x + 7y + 2 = 0 and at unit distance from the point (1, -1).

The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (– 4, 1). Find an equation of the legs (perpendicular sides) of the triangle which are parallel to the axes.

Find the new coordinates in each of the following cases if the origin is shifted to the point (-3, -2) by a translation of axes. (i) (1, 1)  (ii) (0, 1)  (iii) (5, 0)  (iv) (-1, -2)  (v) (3, -5)

Find what the following equation become when the origin is shifted to (1, 1). (i) x²+xy-3y²-y+2=0, (ii) xy-y²-x+y=0, (iii) xy-x-y+1=0