Geometry | Unit 6 | Lesson 16: Weighted Averages in a Triangle | Practice Problems

Triangle ABC and its medians are shown. Select all statements that are true.

• The medians intersect at (1/3, 2).

• The medians and altitudes are the same for this triangle.

• An equation for median AE is y=6/7(x+2).

• Point G is 2/3 of the way from A to E.

• Median BF is congruent to median CD.

Tags

CCSS.HSG.CO.C.10

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

Tags

CCSS.HSG.CO.C.10

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

• 1:2

• 1:1

• HK:KE

• GH:HF

• GK:KJ

Tags

CCSS.HSG.CO.C.10

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

Tags

CCSS.HSG.GPE.B.6

Graph the image of quadrilateral ABCD under a dilation using center A and scale factor 1/3.

Tags

CCSS.8.G.A.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.

Tags

CCSS.6.G.A.3

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.

Tags

CCSS.8.EE.C.8B

A parabola has focus (-3,2) and directrix y=-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

Tags

CCSS.HSG.GPE.A.2