Classify figures by coordinates Triangle \( A B C \) has the following vertices: . \( A(1,9) \) . \( B(11,-7) \) - \( C(-9,3) \) Is triangle \( A B C \) a right triangle, and why? Choose 1 answer (A) Yes, because \( \overline{A B} \perp \overline{A C} \). (B) Yes, because \( \overline{A B} \perp \overline{B C} \). (C) No, because \( \overline{A B} \) is longer than \( \overline{A C} \). (D) No, because \( \triangle A B C \) doesn't have a pair of perpendicular sides. (Delated content

To determine whether triangle \( ABC \) is a right triangle, we can use the concept of slopes. If two sides are perpendicular, the product of their slopes must equal -1. The slope calculations show us that neither pair of sides formed by vertices A, B, and C meet this criteria, confirming that triangle \( ABC \) does not have any right angles. Additionally, there’s a quick way to verify the triangle's characteristics using the Pythagorean theorem. By calculating the lengths of all three sides using the distance formula, we can confirm that the sum of the squares of the two shorter sides does not equal the square of the longest side, thus solidifying that triangle \( ABC \) isn't a right triangle at all!