Q12 of 53 Page 122

Show that the □PQRS formed by P(2,1), Q(-1,3), R(-5,-3) and S(-2,-5) is a rectangle.

According to the distance formula, the distance 'd' between two points (a,b) and (c,d) is given by
 .....(1)


Slope of a line between two points (a,b) and (c,d) is



Note: If the Product of slopes of two lines = -1 then they are perpendicular to each other.


PQ = =


QR = =


RS = =


SP = =


Slope PQ =


Slope QR =


Slope RS =


Slope SP =


As opposite sides are equal and parallel and perpendicular to each other, points form a rectangle.


More from this chapter

All 53 →
10

Show that the line joining the points A(4, 8) and B(5, 5) is parallel to the linejoining the points C(2,4) and D(1,7).

 11

Show that points P(1,-2), Q(5,2), R(3,-1), S(-1,-5) are the vertices of aparallelogram.

 13

Find the lengths of the medians of a triangle whose vertices are A(-1,1), B(5, -3) and C(3, 5).

 14

Find the coordinates of centroid of the triangles if points D(-7,6),E(8,5) andF(2, -2) are the mid points of the sides of that triangle.