Question

using point symmetry about the origin
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)

Explanation:

Step1: Recall point - symmetry rule

If a point $(x,y)$ has point - symmetry about the origin, its symmetric point is $(-x,-y)$.

Step2: Find symmetric points of given vertices

For the point $(2,6)$, its symmetric point about the origin is $(-2,-6)$ since $x = 2,y = 6$ and $-x=-2,-y = - 6$.
For the point $(-1,2)$, its symmetric point about the origin is $(1,-2)$ since $x=-1,y = 2$ and $-x = 1,-y=-2$.

Answer:

$(-2,-6)$ and $(1,-2)$