Triangle \( A B C \) has the following vertices: - \( A(-4,6) \) - \( B(6,6) \) Is triangle \( A B C \) an equilateral triangle, and why? Choose 1 answer: (A) Yes, because \( A B=B C=A C \). (B) Yes, because \( \overline{A B} \perp \overline{A C} \). (C) No, because \( \overline{B C} \) is longer than \( \overline{A B} \). (D) No, because \( \overline{B C} \) is not perpendicular to \( \overline{A B} \).

First, let's take a closer look at the vertices of triangle \( ABC \). With points \( A(-4,6) \) and \( B(6,6) \), we can easily see they lie on a horizontal line since they have the same \( y \)-coordinate. The length of segment \( \overline{AB} \) can be calculated as \( |6 - (-4)| = 10 \). However, we lack the coordinates for point \( C \) to determine if triangle \( ABC \) is equilateral (which requires all sides equal). Therefore, we cannot confirm that \( A B = B C = A C \), nor can we determine perpendicularity without knowing \( C \). Now, considering the options, we can actually dismiss them based on our findings. Option (A) can't be true without knowing \( C \), and options (B) and (D) require \( \overline{A C} \) and \( \overline{B C} \). So you're left with option (C) being plausible, simply because we suspect \( \overline{B C} \) could be longer given we have no equal side lengths established, concluding that triangle \( ABC \) cannot be equilateral since we can't prove all sides are equal. Thus, the best answer here is (C). In summary, the answer is (C) No, because \( \overline{B C} \) is longer than \( \overline{A B} \).