6.3 Centroid

6.3 Centroid

Assessment

Flashcard

Mathematics

10th Grade

Practice Problem

Hard

Created by

Wayground Content

FREE Resource

Student preview

quiz-placeholder

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the centroid of a triangle?

Back

The centroid of a triangle is the point where the three medians intersect. It is also the center of mass of the triangle and is located at the average of the vertices' coordinates.

2.

FLASHCARD QUESTION

Front

How do you calculate the coordinates of the centroid of a triangle with vertices (x1, y1), (x2, y2), (x3, y3)?

Back

The coordinates of the centroid (G) can be calculated using the formula: G = \left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right).

3.

FLASHCARD QUESTION

Front

If the vertices of a triangle are (2, 3), (4, 5), and (6, 7), what are the coordinates of the centroid?

Back

The centroid is G = \left(\frac{2 + 4 + 6}{3}, \frac{3 + 5 + 7}{3}\right) = (4, 5).

4.

FLASHCARD QUESTION

Front

What is the relationship between the centroid and the lengths of the segments created by the centroid on the medians?

Back

The centroid divides each median into two segments, with the segment connecting the vertex to the centroid being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

5.

FLASHCARD QUESTION

Front

If point P is the centroid of triangle ABC and PL = 18, what is the length of BP?

Back

BP = 36, since the centroid divides the median in a 2:1 ratio.

6.

FLASHCARD QUESTION

Front

If BP = 10, what is the length of BL if P is the centroid?

Back

BL = 15, as the centroid divides the median in a 2:1 ratio.

7.

FLASHCARD QUESTION

Front

What is the formula for the length of a median in a triangle with vertices (x1, y1), (x2, y2), (x3, y3)?

Back

The length of the median from vertex A to side BC can be calculated using the formula: m_a = \sqrt{\frac{2b^2 + 2c^2 - a^2}{4}}, where a, b, and c are the lengths of the sides.

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Google

Continue with Google

Email

Continue with Email

Classlink

Continue with Classlink

Clever

Continue with Clever

or continue with

Microsoft

Microsoft

Apple

Apple

Others

Others

Already have an account?