Question

drag the vertices of $\triangle ijk$ to form a scalene obtuse triangle.

Explanation:

Step1: Recall triangle definitions

A scalene triangle has all sides of different lengths, and an obtuse triangle has one angle greater than $90^\circ$ (and less than $180^\circ$). The current triangle has all acute angles, so we need to adjust vertices to create one obtuse angle while keeping all sides unequal.

Step2: Adjust vertices for obtuse angle

Drag one vertex (e.g., vertex $I$) outward away from the side $JK$ such that one internal angle (e.g., $\angle J$ or $\angle K$) becomes greater than $90^\circ$. Ensure that after adjustment, the lengths of $IJ$, $JK$, and $KI$ remain all distinct (which they will be with this adjustment as long as we don't make any sides equal).

Step3: Verify the triangle

Confirm: 1) All side lengths are different (scalene), 2) One internal angle measures between $90^\circ$ and $180^\circ$ (obtuse).

Answer:

A valid scalene obtuse triangle is formed when one internal angle of $\triangle IJK$ is greater than $90^\circ$, and all three side lengths are distinct. For example, drag vertex $I$ so that $\angle J$ measures $110^\circ$, with side lengths such as $JK=5.39$, $IJ=8.1$, $KI=10.2$ (specific values can vary as long as the scalene and obtuse conditions are met).