### Understanding the Centroid of a TriangleIn the following diagram, point $ Z $ is identified as the centroid of triangle $ \triangle UVW $.#### Diagram Explanation:- The triangle $ \triangle UVW $ is depicted with vertices labeled $ U $, $ V $, and $ W $.- Inside the triangle, point $ Z $ is marked as the centroid.- Three segments are shown: - Segment $ UW $ - Segment $ WV $ - Segment $ UV $- Medians of the triangle (segments from each vertex to the midpoint of the opposite side) intersect at point $ Z $.The centroid (point $ Z $) of a triangle is the point where all three medians intersect. It is also known as the "center of mass" and is located at a position where it balances the triangle.### Question:Which of the following geometric constructs intersect at the centroid $ Z $ of the triangle $ \triangle UVW $?A. MediansB. AltitudesC. Angle BisectorsD. Perpendicular Bisectors### Options:- **A** - Medians: The correct answer. The centroid is the intersection point of the medians of the triangle.- **B** - Altitudes: These are segments from each vertex perpendicular to the opposite side, intersecting at the orthocenter.- **C** - Angle Bisectors: These intersect at the incenter, which is the center of the inscribed circle.- **D** - Perpendicular Bisectors: These intersect at the circumcenter, which is the center of the circumscribed circle.#### Select the correct option to check your understanding of the geometrical properties of the centroid.

It is known that in a triangle, the line drawn from one vertex to the opposite side dividing the…

Answered: Z is the centroid of AUVW. Zis the…

Z is the centroid of AUVW. Zis the intersection of the triangle's A. medians O B. altitudes C. angle bisectors O D. perpendicular bisectors

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

See similar textbooks

Related questions

Q: Use triple itegral.in cylindrical. coordinates to mass of a- find. sphere .with density S. te. ass…

A: Mass is calculated by tripple integral of density.

Q: What is the area of the triangle ABC with vertices А(1,2, 3), В(2,4, 3), C(1, 2, 0) ? Select one: O…

Q: RT and UW are parallel lines. Q V W Which angles are adjacent angles? R.

Q: The points P: (-2,0,0), Q: (0,1,1) and R: (1,2,1) are givena. determine the angle in the triangle…

A: Solution a) To determine the angle at corner Q in triangle ΔPQR, we can use the dot product…

Q: find the area of a triangle. given the points A, B, and C. Plot the points A= (0,2,6), B= (8,2,2),…

Q: The area of the triangle with vertices (1,1), (8, 7), (8, 1) is Select one: O a. 21 O b. 20 O c. 42…

A: The area of a triangle with vertices x1, y1, x2, y2 and x3, y3 is calculated by the following…

Q: Let triangle ABC be an equilateral triangle of sides 100 units long. Find the coordinates of points…

Q: If D is the triangle with vertices (0,0), (40,0), (40,25), then dA=

A: The triangle D is with the vertices (0,0), (40,0) & (40,25). The line passing through (0,0) and…

Q: What kind of triangle on its sides form the vertices (0, –5. 5), (1, –2, 4), (3, 4, 2). B) Calculate…

Q: Given the following points: P (1, 0, 5), Q(3,5,6) and R(-1,2,8) makes up a triangle. Find the…

Q: P(1,0,4), Q(2,4,6) and R(-1,3,6) makes up a triangle find a. perimeter of the triangle b. area of…

Q: The vertices of AWIN are W(2, 1), I(4, 7), and N(8, 3). Using coordinate geometry, show AWIN is an…

Q: Find the area of a parallelogram with corner points at (2,1), (4,5), (7,5), and (5,1) Area: =

A: Area of a parallelogram is given by absolute value of the determinant of the adjacent vectors u and…

Q: S R 1 V U W Question 5 (1 point) If T and X are the respective midpoints for SU and RW then what is…

A: For Question 5, Since T and X are midpoints of SU and RW, respectively, VX is half the length of SU…

Q: M

A: Given figure is: Chord: A line segment that joins any two points on the circumference of the…

Q: 4. Find the center of (a) V; (b) Q8-

A: We have to find centre of following groups: Definition: Let G is a group then centre of G denoted by…

Q: Use the figure below to answer the question. P E N Name the intersection of planes P and N? B О ВА O…

A: Consider the figure

Q: Choose two figures which are topologically equivalent to each other

A: We can say A and B are topologically equivalent or homeomorphism if there exist a continuous,…

Q: KM and NP are parallel lines. K Which angles are corresponding angles? ZMLO and ZKU ZMLO and ZPOQ…

Q: . Prove that the figure with the coordinates given is a parallelogram. (Use diagonals bisect each…

A: Note : A & C are diagonally opposite points And, B & D are diagonally opposite points.

Q: Find the area of a triangle whose coordinates are A (1,1), B (3,-3), C (5,3)

Q: The triangle vertices are given by the points A(3, 5, 7), B(a, 5, 5), and C(5,5, 4), if the area of…

A: We know that area of a triangle is half of a parallelogram.

Q: 2. Show work to determine if the points A(1, –1,4), B(2, 1, –1), and C(4, 0,5) form a right…

Q: Consider a triangle with vertices X, Y, and Z.

A: Definition used - Triangle law of vector addition - According to…

Q: What kind of angles are a and b? O supplementary O Complementary

Q: Sled kites rely on wind pressure to retain the shape of the sail. Each consists of a single square…

A: Consider the given figure.

Q: Find the lengths of the sides of the triangle given by the points P(2, –1,0) and Q(4,1,1) and R(4,…

Q: 4. The coordinates of a quadrilateral composed in quadrant of the coordinate plane are (0, 0), (0,…

A: Given Four points ( 0 , 0 ) , ( 0 , C ) , ( b , c ) , ( b , 0 ) Distance between two points is…

Question

### Understanding the Centroid of a Triangle

In the following diagram, point $ Z $ is identified as the centroid of triangle $ \triangle UVW $.

#### Diagram Explanation:
- The triangle $ \triangle UVW $ is depicted with vertices labeled $ U $, $ V $, and $ W $.
- Inside the triangle, point $ Z $ is marked as the centroid.
- Three segments are shown:
- Segment $ UW $
- Segment $ WV $
- Segment $ UV $
- Medians of the triangle (segments from each vertex to the midpoint of the opposite side) intersect at point $ Z $.

The centroid (point $ Z $) of a triangle is the point where all three medians intersect. It is also known as the "center of mass" and is located at a position where it balances the triangle.

### Question:
Which of the following geometric constructs intersect at the centroid $ Z $ of the triangle $ \triangle UVW $?

A. Medians

B. Altitudes

C. Angle Bisectors

D. Perpendicular Bisectors

### Options:
- **A** - Medians: The correct answer. The centroid is the intersection point of the medians of the triangle.
- **B** - Altitudes: These are segments from each vertex perpendicular to the opposite side, intersecting at the orthocenter.
- **C** - Angle Bisectors: These intersect at the incenter, which is the center of the inscribed circle.
- **D** - Perpendicular Bisectors: These intersect at the circumcenter, which is the center of the circumscribed circle.

#### Select the correct option to check your understanding of the geometrical properties of the centroid.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Inequality$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

Similar questions

Which sets of point are collinear?
FGH is a right angled triangle with shortest sides FH=6cm and FG=8cm. I, J, and K are the mid points of the sides GH, FHand FG respectively. What is the perimeter of the triangle IJK? H F G
Please answer both subparts. I will really upvote
Use the image to answer the question
2. Find the area of the triangle formed by the lines 5x + y – 14 = 0, x+ 7y+38 = 0, and 9x – 5y + 2 = 0
4. Consider the following figure: A(1,1,0) D B(-1,-1,-1) C(2,2,0) a) Find the coordinate of D if ABCDis parallelogram b) Calculate the area of parallelogram.
The geometry club designed a new shirt for club members. The pocket is formed by a rectangle with vertices at R(2, 1), S(10, 1), T(10, 10), and U(2, 10). The geometry club logo will be placed on a quadrilateral formed by connecting the midpoints of the sides of the rectangular pocket. a. Find and label the coordinates of the vertices of the interior quadrilateral. b. Make a conjecture to classify the interior quadrilateral that will be used for the geometry club logo using lengths and slopes of the sides.
Vertices of a triangle PQR have coordinates: P (2, 1, -1), Q (6, 4, 2) and R (5, 3, 1). Use the Dot product to find the angle at the vertex P. Draw the triangle and label the angle.