Centroid and Orthocenter

Question 1

In which figure is point G an orthocenter?

Revolt · Accepted Answer

Triangle H J K is shown. Lines are drawn from each point to the opposite side to form right angles and the lines intersect at point G.

Question 2

The steps shown can be used to prove that the medians of a triangle meet at a point.1. Define segments BD and CE as medians of triangle ABC.2. Write linear equations for and .3. Use a system of linear equations to solve for the coordinates of intersection point G.4. Write the equation of .5. Write an expression for the midpoint of BC, point F. 6. Show that point F lies on .7. ?

Revolt · Accepted Answer

Show that AF is the median of BC.

Question 3

In triangle ABC, EG = x inches and BG = (5x - 12) inches. [Figure may not be drawn to scale]

Revolt · Accepted Answer

12 inches

Question 4

Point G is the centroid of triangle ABC. The length of segment CG is 6 units greater than the length of segment DG.

Revolt · Accepted Answer

18 units

Question 5

A centroid is the intersection of three

Revolt · Accepted Answer

medians in a triangle.

Question 6

An orthocenter is the intersection of three

Revolt · Accepted Answer

altitudes in a triangle.

Question 7

In the diagram, GB = 2x + 3..

Revolt · Accepted Answer

15 units

Question 8

In which type of triangle is the orthocenter on the perimeter of the triangle?

Revolt · Accepted Answer

a right triangle

Question 9

If an orthocenter lies inside of a triangle, then the triangle must be

Revolt · Accepted Answer

acute.

Question 10

In triangle NLM, point S is the centroid, QS = (3x – 5) cm, and NS = (4x) cm.

Revolt · Accepted Answer

20 cm

Centroid and Orthocenter Answers

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