Question

Please Help me PLLLEEEAAASSSEEEEE

The coordinates of the vertices of quadrilateral GOLF are G(3, -1), O(1, -6), L(-4, -4), and F(-2, 1). Prove or disprove that the quadrilateral is a square.

Identify the characteristics of a square (there are 3). Use algebra to discover if this quadrilateral has those characteristics, or not.

Answer 1

A quadrilateral become square if all the sides joining the co-ordinate of quadrilateral is equal

Explanation:

Here the given co-ordinate of quadrilateral are

G (3, -1) O(1, -6)

L(-4, -4) F(-2, 1)

Line GF =
`√((3+2)^2+(-1-1)^2)`

GF =
`√(29)`

Similarly for line OG, OL, FL

OG =
`\sqrt{(1-3)^2 +(-6+1)^2`

OG =
`√(29)`

OL =
`√((-4-1)^2+(-6+4)^2)`

OL =
`√(29)`

And

FL =
`√((-4+2)^) +(-4+1)^2`

FL =
`√(29)`

all the sides of quadrilateral GF, OG, OL, FL all equal to
`√(29)`

As all the sides are equal so quadrilateral become square Answer