Coordinate Geometry

Find the distance between the points A(3, 4) and B(7, 1).

What is the midpoint of the line segment joining points P(2, -3) and Q(8, 5)?

Find the slope of the line passing through points (1, 2) and (4, 8).

Find the equation of the line passing through (0, -3) and having slope 4.

If the points A(1, 2), B(4, k), and C(7, 8) are collinear, find the value of k.

Find the area of the triangle formed by points A(0, 0), B(4, 0), and C(4, 3).

Find the coordinates of the point which divides the line segment joining A(2, 3) and B(8, 7) internally in the ratio 3:2.

Find the equation of the circle with center at (2, -3) and passing through point (5, 1).

Find the equation of the line perpendicular to 3x - 4y + 7 = 0 and passing through (1, 2).

Find the coordinates of the foot of the perpendicular drawn from point P(3, 4) to the line 5x - 12y + 9 = 0.