Triangle \(ABC\) and its medians are shown. Write an equation for median \(AE\).

Given \(A(1,2)\) and \(B(7,14)\), find the point that partitions segment \(AB\) in a \(2:1\) ratio.

A quadrilateral has vertices \(A(0,0), B(4,6), C(0,12),\) and \(D(\text-4,6)\). Mai thinks the quadrilateral is a rhombus and Elena thinks the quadrilateral is a square. Do you agree with either of them? Show or explain your reasoning.  

The image shows a graph of the parabola with focus \((\text-3,\text-2)\) and directrix \(y=2\), and the line given by \(y=\text-3\). Find and verify the points where the parabola and the line intersect.

For each equation, is the graph of the equation parallel to the line shown, perpendicular to the line shown, or neither?

1. \(y=0.25x\)
2. \(y=2x - 4\)
3. \(y-2 = \text-4(x-3)\)
4. \(2y + 8x = 7\)
5. \(x-4y=3\)

Write two equivalent equations for a line with \(x\)-intercept \((3,0)\) and \(y\)-intercept \((0, 2)\). 

Parabola A and parabola B both have the line \(y=\text-2\) as the directrix. Parabola A has its focus at \((3, 4)\) and parabola B has its focus at \((5,0)\). Select all true statements.