# 3 ways to calculate the center of gravity of a triangle 3 ways to calculate the center of gravity of a triangle

The center of gravity, also called the centroid, is the point at which the mass of a triangle is in equilibrium. To help you better understand this concept, imagine you have a triangular shaped tile above the tip of a pencil. The tile will be kept in balance if and only if the pencil is placed just in the center of its gravity. This concept may be necessary in several fields of application, such as in the field of engineering and design. To find the point of gravity of a triangle, you will only have to use simple geometric operations.

## Steps

### Method 1 of 3: Use the intersection of medians method #### Step 1. Find the midpoint on another side of the triangle

To do this, measure the side in question and divide the length by two. Write the letter A on the midpoint.

• Suppose one side of a triangle is 10 cm. The midpoint will be 5cm because 10/2 = 5 { displaystyle 10/2 = 5} #### Step 2. Find the midpoint on another side of the triangle

To do this, you need to measure the length of this segment and divide by two. Write the letter B in the middle of this segment.

• For example, if another side of the triangle is 12cm in length, the midpoint will be 6cm because 12/2 = 6 { displaystyle 12/2 = 6} #### Step 3. Draw a line from the middle of each side to the opposite vertex

These two lines represent the median on each side.

### The vertex is the meeting point of the two sides of the triangle #### Step 4. Draw a point at the intersection of the two midpoints

This point is the center of gravity of your triangle, and is also called the centroid or center of mass.

### Method 2 of 3: Use the 2: 1 ratio #### Step 1. Draw a median of the triangle

In geometry, the median is a line that extends from the middle of a segment to the opposite vertex. You can choose any median of a triangle. #### Step 2. Measure the length of the median

Make sure you measure it properly.

### For example, you can have a median that is 3.6 cm long #### Step 3. Divide the length of the median into three equal parts

You just need to divide by three. Again, be sure to do an exact calculation. If you round the result, you will not find the exact center of gravity.

• For example, if the median is 3.6cm long, you should divide 3.6 by 3: 3.6cm / 3 = 1.2cm { displaystyle 3.6cm / 3 = 1.2cm}

, donc le tiers de cette longueur est égale à 1, 2 cm. #### Step 4. Mark a point on the third of the median from the midpoint

This point represents the centroid of the triangle. The center of gravity always divides a median, which translates to a ratio of 2: 1. In other words, the centroid is one-third of the median distance from the midpoint, and two-thirds of the median distance from the top.

### Method 3 of 3: Use the average of the coordinates #### Step 1. Find the coordinates of all the vertices of the triangle

This trick works, as long as you are working in a coordinate plane. They might already be mentioned in your exercise, or you might have a triangle drawn on a graph with no coordinates. Remember that coordinates are always expressed as (x, y) { displaystyle (x, y)} ### Supposons que vous avez un triangle PQR. Vous devrez retrouver les coordonnées et les réécrire sous cette forme: le point P (3, 5), le point Q (4, 1), le point R (1, 0) #### Step 2. Add the values ​​of the x coordinates

Remember to add the three x coordinates. You will not find the precise value of the center of gravity if you only use two coordinates.

• For example, if your three x coordinates are 3, 4, and 1, add these values ​​(3 + 4 + 1 = 8 { displaystyle 3 + 4 + 1 = 8}

). #### Step 3. Add the y coordinate values

Remember to add the three y coordinates.

• For example, if the three y coordinates of your exercise are 5, 1, and 0, add these values ​​(5 + 1 + 0 = 6 { displaystyle 5 + 1 + 0 = 6}

). #### Step 4. Calculate the average of the x and y coordinates

These coordinates represent the center of gravity of the triangle, also called the centroid or center of mass. To calculate the average, add the coordinates and divide the result by 3.

• For example, if the sum of the coordinates in x is equal to 8, the average of the coordinates in x will be equal to 8/3 { displaystyle 8/3}

. Si la somme des coordonnées en y est égale à 6, la moyenne des coordonnées sera égale à 6/3{displaystyle 6/3}

, ou 2{displaystyle 2}  #### Step 5. Represent the centroid

By following this method, the center of gravity is nothing more than the average of the x and y coordinates.

• So for our example, the centroid is the point (8/3, 2) { displaystyle (8/3, 2)}