Answer:
Option d. is correct
Step-by-step explanation:
Given Points : \(A\left ( 0,\sqrt{27} \right )\,,\,B\left ( -3,0 \right )\,,\,C\left ( 3,0 \right )\)
We need to choose the most specific name for the polygon formed by points A, B and C .
Solution:
We know that a regular triangle is a polygon with three equal sides.
Also, for points \(P\left ( x_1,y_1 \right )\,,\,Q\left ( x_2\,,\,y_2 \right )\), distance is given by \(\sqrt{\left ( x_2-x_1 \right )^2+\left ( y_2-y_1 \right )^2}\).
\(AB=\sqrt{\left ( -3-0 \right )^2+\left ( 0-\sqrt{27} \right )^2}=\sqrt{9+27}=\sqrt{36}=6\,\,units\\BC=\sqrt{\left ( 3+3 \right )^2+\left ( 0-0 \right )^2}=\sqrt{36}=6\,\,units\\AC=\sqrt{\left ( 3-0 \right )^2+\left ( 0-\sqrt{27} \right )^2}=\sqrt{9+27}=\sqrt{36}=6\,\,units\)
As AB = BC =AC, it's a regular triangle.
Option d. is correct
