## Co-ordinate Geometry

Hello all, In the problem specified below, I felt that there is no statement existing which is true. But, the answer provided for the problem in the source site is different. Can someone help me in solving this out? Which of the following is / are true? (1) (a,a),(a,a),(3a,3a) are the vertices of an equilateral triangle. (2) (0,2),(3,1),(0,4),(3,1) are the vertices of a square. (3) (0,1),(2,3),(6,8),(8,3) are the vertices of a rectangle. In the solution provided the answer is given based on the distance between the points. But, virtually plotting the given vertices on a graph will not yield the shapes specified. Kindly, help me in knowing the way of solving the problem out. Thanks in advance.

## (a) (a,a),(a,a),(3a,3a) are

(a) (a,a),(a,a),(3a,3a) are the vertices of an equilateral triangle. I think its (a,a),(2a,2a),(3a,3a) – all theses points lies on a straight line so no question of equilateral triangle. (b)(0,2),(3,1),(0,4),(3,1) – two points are same –chk the question once again There are many ways to approach this and I started with most simple condition – if these are the vertices of square then (i) the angle between one point and other two points should be 90 { if all the points satisfies then I ll check the second condition (ii) length of all sides should be same} I took point (0,2), none of the other points passing through this line and other line has an angle of 90. That’s enough to discard this option (c) Same to above(b) You are correct the answer is none of the above