Question

Choose the most specific name for the polygon formed by points a, b, and c.
a. trapezoid
b. isosceles triangle
c. scalene triangle
d. regular triangle

Answer 1

The answer is d. regular triangle (also known as equilateral triangle)
All sides are length 6.

Answer 2

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