Final answer:
The question pertains to finding whether triangle ABC given its vertices A(2,0), B(4,4), and C(6,3) is isosceles or right. This can be determined by calculating the lengths of the sides and checking for equality (for isosceles) or by applying the Pythagorean theorem (for right angle).
Step-by-step explanation:
The subject is about the classification of a triangle based on its vertices A, B, and C. A triangle's classification as isosceles or right can be determined by examining the lengths of its sides. In an isosceles triangle, two sides are of equal length, whereas in a right triangle, the square of the length of one side (the hypotenuse) is equal to the sum of the squares of the lengths of the other two sides (Pythagorean theorem).
To find out who is correct between Zackery and Verna, we have to calculate the distances between points A, B, and C. To confirm if it is an isosceles triangle or a right triangle, we then examine these distances. For example, the distance between A and B which we represent as AB can be calculated using the distance formula as follows:
AB = sqrt[(x2-x1)*(x2-x1) + (y2-y1)*(y2-y1)]
If, after doing this for all three pairs of points (AB, BC, and AC), we find two sides to be equal in length, then it is an isosceles triangle, if it fulfills the Pythagorean theorem, then it is a right triangle.
Learn more about Triangle classification