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

Option d. is correct

Explanation:

Given Points :
`A\left ( 0,√(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
`√(\left ( x_2-x_1 \right )^2+\left ( y_2-y_1 \right )^2)`.

`AB=\sqrt{\left ( -3-0 \right )^2+\left ( 0-√(27) \right )^2}=√(9+27)=√(36)=6\,\,units\\BC=√(\left ( 3+3 \right )^2+\left ( 0-0 \right )^2)=√(36)=6\,\,units\\AC=\sqrt{\left ( 3-0 \right )^2+\left ( 0-√(27) \right )^2}=√(9+27)=√(36)=6\,\,units`

As AB = BC =AC, it's a regular triangle.

Option d. is correct