Lesson 16

Triangle $ABC$ and its medians are shown.

Select all statements that are true.

The medians intersect at $\left(\frac{1}{3}, 2\right)$.

The medians and altitudes are the same for this triangle.

An equation for median $AE$ is $y=\frac{6}{7}(x+2)$.

Point $G$ is $\frac{2}{3}$ of the way from $A$ to $E$.

Median $BF$ is congruent to median $CD$.

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

8 units

5 units

3 units

2 units