Do (1,−5) and (−5, 1) lie the same quadrant? Justify your answer.

Find the distance between the points (−2,−3) and (4, 1).

Suppose (a, b) is at a distance of 5 units from (3,−5). What equation do a and b satisfy?

Show that the distance of a point P(x, y) from the origin is p(x2 + y2)

Find the coordinates of the point which divides the line joining (2, 4) and (6, 8) in the ratio 2:3?

Show that the point A(4, 6), B(7, 7), C(10, 10) and D(7, 9) are the vertices of a parallelogram?

Find the slope of the lines passing through the points given below i) (3, 2) and (1, 0), ii) (5, 0) and (−1, 1), iii) (−4,−4) and (5,−5), iv) (3,−3) and (6,−1)

Plot the following equations on a plane:

i) y = x

ii) 3y + 5x − 1 = 0)