Question

in which figure is point g a centroid?

Explanation:

The centroid of a triangle is the intersection point of its medians. A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.

• In the first triangle (with vertices A, B, C), we need to check if the lines through G connect vertices to midpoints of opposite sides.
• In the second triangle (with vertices D, E, F), the lines through G appear to connect each vertex (D, E, F) to the midpoint of the opposite side (e.g., D to midpoint of FE, F to midpoint of DE, E to midpoint of DF). This matches the definition of a centroid as the intersection of medians. The first triangle has a right angle at C, and the lines through G do not seem to be medians (e.g., the line from A to the midpoint of CB? Wait, no—wait, the second triangle: the segments from D to FE's midpoint, F to DE's midpoint, and E to DF's midpoint intersect at G, which is the centroid. The first figure: the lines through G—one from A, one from B, one from C—but are they medians? The second triangle's segments are medians (connecting vertex to midpoint of opposite side), so G is the centroid there.

Answer:

The figure with vertices D, E, F (the second triangle) has point G as the centroid.