Question

The points (
,
), (
,
), and (
,
) are plotted on the coordinate plane.

Yari plots a fourth point at (
,
) and claims the figure is a square.

Jessica argues that the figure cannot be a square because all points are not the same distance from zero.

image


Who is correct and why?


Yari because the horizontal and vertical distance between each is
units, making all the sides of the figure the same length.

Jessica because all points are not the same distance from the
- and
-axes.

Yari because with the point (
,
), he plotted four points on the coordinate plane and it takes four points to create a square.

Jessica because all points do not have the same absolute value and therefore cannot create a square.

Answer 1

Yari is correct.

A square is determined by having four equal side lengths and right angles (or equivalently equal side lengths and perpendicular adjacent sides). Jessica’s claim about all points being the same distance from the origin (or from the axes / having the same absolute values) is irrelevant — a square does not have to be centered at the origin or have equal distances to the axes. Also, simply having four points is not enough to guarantee a square unless those points give equal sides and right angles. The plotted fourth point does produce equal horizontal and vertical offsets (so adjacent sides are equal and perpendicular), so the figure is a square.