5-3 Medians and Altitudes

Find the centroid of the triangle with vertices at (1, 2), (4, 5.5), and (7, 3).

• (3, 5)

• (2, 4)

• (4, 3.5)

• (5, 4.5)

Identify the centroid of a triangle with vertices at (2, 4), (6, 8), and (10, 12).

• (8, 6)

• (6, 8)

• (12, 10)

• (2, 4)

Determine the orthocenter of a triangle with vertices at (-1, 0), (3, 4), and (5, -2).

• (0, 3)

• (3, 0)

• (2, 2)

• (4, 1)

Calculate the orthocenter of a triangle with angles measuring 60°, 60°, and 60°.

• The orthocenter is at the same point as the centroid.

• The orthocenter is always outside the triangle.

• The orthocenter is located at the midpoint of the triangle's longest side.

• The orthocenter is the same as the incenter of the triangle.

Which of the following statements are true for △ABC? Select all that apply.

• ​AH is an altitude

• ​IH is a median

• JC is a median

• The medians and altitudes intersect at the same point

In △JKL, what are PK and RJ?

• ​PK = 10, RJ = 6

• ​PK = 15, RJ = 9

• ​PK = 6, RJ = 10

• ​PK = 9, RJ = 15

Select the true statement about △ABC

• AD is an altitude of the triangle

• BE is a median of the triangle

• X is the orthocenter of the triangle

• X is the centroid of the triangle

A triangle with vertices at (3, 4) and (9, 17) has centroid at (8, 16). What are the coordinates of its third vertex?

• (5, 10)
• (12, 27)

• (7, 14)
• (10, 20)

Organize these options into the right categories

Groups:

(a) median

,

(b) altitude

,

(c) neither

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Match the following centers of triangles.

• Circumcenter

• 
• Incenter

• 
• Orthocenter

• 
• Centroid

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