Triangle \(ABC\) has vertices at \((\text-2,0), (\text-1,6),\) and \((6,0)\). What is the point of intersection of the triangle’s medians?

Triangle \(EFG\) and its medians are shown.

Match each pair of segments with the ratios of their lengths.

Given \(A(\text-3,2)\) and \(B(7,\text-10)\), find the point that partitions segment \(AB\) in a \(1:4\) ratio.

Graph the image of quadrilateral \(ABCD\) under a dilation using center \(A\) and scale factor \(\frac{1}{3}\).

A trapezoid is a quadrilateral with at least one pair of parallel sides. Show that the quadrilateral formed by the vertices \((0,0), (5,2), (10,10),\) and \((0,6)\) is a trapezoid.

Here are the graphs of the circle centered at \((0,0)\) with radius 6 units and the line given by \(2x+y=11\). Determine whether the circle and the line intersect at the point \((3,5)\). Explain or show your reasoning.

A parabola has its focus at \((\text-3,2)\), and its directrix is \(y=\text-3\). The point \((a,5)\) is on the parabola. How far is this point from the focus?