Centroid and Orthocenter

Question 1

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

Revolt · Accepted Answer

20 cm

Question 2

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

Revolt · Accepted Answer

12 inches

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

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.

Revolt · Accepted Answer

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

Question 5

In triangle DEF, CG = (x + 5) units and DG = (3x - 2) units.[Figure may not be drawn to sacle]

Revolt · Accepted Answer

34 units

Question 6

A centroid is the intersection of three

Revolt · Accepted Answer

medians in a triangle.

Question 7

An orthocenter is the intersection of three

Revolt · Accepted Answer

altitudes in a triangle.

Question 8

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

Revolt · Accepted Answer

acute.

Question 9

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

Revolt · Accepted Answer

9 inches

Question 10

In triangle NQL, point S is the centroid, NS = (x + 10) feet, and SR = (x + 3) feet.

Revolt · Accepted Answer

7 feet

Centroid and Orthocenter Answers