IM Geo.6.16 Practice: Weighted Averages in a triangle

Select all statements that are true.

Triangle  has vertices at , , and .What is the point of intersection of the triangle’s medians?

Triangle and its medians are shown. Match each pair of segments with the ratios of their lengths.

Given  and , find the point that partitions segment  in a  ratio.

A trapezoid is a quadrilateral with at least one pair of parallel sides. Show that the quadrilateral formed by the vertices , , , and  is a trapezoid.

Here are the graphs of the circle centered at  with radius 6 units and the line given by . Determine whether the circle and the line intersect at the point . Explain or show your reasoning.

A parabola has focus  and directrix . The point  is on the parabola.How far is this point from the focus?