Zigzag Test 4 Q4: Ellipse and Locus of Midpoint

This example demonstrates the construction of an ellipse and the locus of midpoints of segments connecting a moving point on the ellipse to fixed points, as part of Zigzag Test 4 Question 4. The core mathematical concepts involve ellipse geometry, midpoint coordinates, and locus generation. Construction steps use GeoGebra commands: Point to create points A, B, C, etc., Ellipse to define ellipse c, Intersect to find intersection points, Line to draw lines, and Midpoint to compute midpoints. By tracing midpoints D, E, F, G, the resulting locus is visualized. Suitable for high school analytic geometry or math competition preparation, this example helps students intuitively understand how midpoint loci relate to ellipse parameters and enhances dynamic geometric exploration skills.