Question

A quadrilateral with vertices (2, 6) and (–1, 2) has point symmetry about the origin. What are the other vertices of the quadrilateral? (6, 2) and ( 2, –1) (–2, 6) and (1, 2) (–2, –6) and (1, –2) (2, 6) and (–1, 2)

Answer 1

Point symmetry is a 180 degree rotation around the origin.

It maps (x,y) to (-x,-y).

So (2,6) and (-1,2) map to

(-2,-6) and (1,-2), third choice

Answer 2

Answer with explanation:

The two vertices of Quadrilateral are which has point of symmetry about the origin =(2, 6) and (–1, 2)

Point of Symmetry about origin means distance from origin to the Original point and when this point is rotated by an Angle of 180° from that point , the two are equidistant from Origin.

Point (2,6) when rotated by an Angle of 180° ,it goes in third Quadrant having vertices = (-2, -6)

Similarly, When Point (-1,2) when rotated by an Angle of 180° ,it goes in fourth Quadrant having vertices = (1,-2)

⇒Distance of points (2,6) and (-2,-6) from Origin are Same.

⇒Distance of points (-1,2) and (1,-2) from Origin are Same.

So,the Other vertices of the quadrilateral are

 ⇒  (–2, –6) and (1, –2)