Question

When the coordinates (1, 1), (4, 4), (7, 1), and (4, −2) are joined, which shape is formed?

Answer 1

A square is made by those coordinates

Answer 2

Answer with explanation:

The coordinates of four points are A(1, 1), B(4, 4), C(7, 1), and D(4, −2).

Plotting the four points in the two dimensional Coordinate plane

When you will plot these points you will get the shape of a Quadrilateral.

`AB=√((4-1)^2+(4-1)^2)\\\\AB=√(9+9)\\\\AB=√(18)\\\\AB=3√(2)\\\\BC=√((7-4)^2+(1-4)^2)\\\\BC=√(9+9)\\\\BC=√(18)\\\\BC=3√(2)\\\\CD=√((7-4)^2+(1+2)^2)\\\\CD=√(9+9)\\\\CD=3√(2)\\\\AD=√((4-1)^2+(-2-1)^2)\\\\AD=√(9+9)\\\\AD=3√(2)`

As all sides are equal, so this can be Square or Rhombus.

Slope between two points (1, 1), and (4, 4) is

`m_(1)=(4-1)/(4-1)\\\\=1\\\\\text{Between }(4,4) \text{and} (7,1)\\\\m_(2)=(4-1)/(4-7)\\\\m_(2)=(-1)/(3)\\\\m_(1)*m_(2)=3*(-1)/(3)\\\\m_(1)*m_(2)=-1`

⇒Prodct of slopes is -1, showing that lines which are sides of Quadrilateral are Perpendicular.

⇒As angle between sides measures 90°.So, the Quadrilateral is Square.

→Square