Question

I NEED HELP PLEASE

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. Explanation is not necessary, but be sure to show all work.

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

Answer 1

Answer:

It is proved that GOLF is a square.

Step-by-step explanation:

If we can prove that all the sides of a quadrilateral are of equal length and any one of the angles is right angle then we will be able to say that the quadrilateral is a square.

Now, given four vertices of the quadrilateral GOLF as G(3, -1), O(1, -6), L(-4, -4), and F(-2, 1).

Hence, length of GO is $\sqrt{(3-1)^{2}+(-1-(-6))^{2}  } =\sqrt{29}$ units.

Length of OL is $\sqrt{(1-(-4))^{2}+(-6-(-4))^{2}  } =\sqrt{29}$ units.

Length of LF is $\sqrt{(-4-(-2))^{2}+(-4-1)^{2}  } =\sqrt{29}$ units.

And the length of FG is  $\sqrt{(3-(-2))^{2}+(-1-1)^{2}  } =\sqrt{29}$ units.

Hence, GO = OL = LF = FG = $\sqrt{29}$ units

Now, the slope of line GO is given by $\frac{-1-(-6)}{3-1} =\frac{5}{2}$.

Again the slope of OL is given by $\frac{-6-(-4)}{1-(-4)} =-\frac{2}{5}$

So, the product of the slopes of GO and OL is = $\frac{5}{2}*(-\frac{2}{5} ) =-1$

Hence, GO ⊥ OL and ∠GOL = 90°

Therefore, it is proved that GOLF is a square. (Answer)