Centroid and Orthocenter

Question 1

A centroid is the intersection of three

Revolt · Accepted Answer

medians in a triangle.

Question 2

Point G is the centroid of triangle ABC. AG = (5x + 4) units and GF = (3x – 1) units.

Revolt · Accepted Answer

51 units

Question 3

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 4

An orthocenter is the intersection of three

Revolt · Accepted Answer

altitudes in a triangle.

Question 5

Triangle H J K is shown. Lines are drawn from each point to the opposite side and intersect at point G to form line segments H C, J E, and K D.

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Point G cannot be a centroid because JG and GE are in the ratio 1:2.

Question 6

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

Revolt · Accepted Answer

a right triangle

Question 7

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 8

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

Revolt · Accepted Answer

acute.

Question 9

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

Revolt · Accepted Answer

15 units

Question 10

In triangle TRS, TZ = (3x) inches and WZ = (2x - 3) inches.[Figure may not be drawn to scale]

Revolt · Accepted Answer

9 inches

Centroid and Orthocenter Answers