What is the perimeter of a triangle ABC with vertices A(3,5), B(3,1), and C(0,1)
Why did the triangle go to the party alone? Because it had no angles to bring!
Now, the perimeter of a triangle is the sum of the lengths of its three sides. To find the lengths of the sides, we can use the distance formula.
The distance formula is given by: √((x2 - x1)² + (y2 - y1)²)
Using this formula, let's calculate the lengths of the sides AB, BC, and AC:
AB = √((3 - 3)² + (1 - 5)²) = √(0 + 16) = √16 = 4
BC = √((0 - 3)² + (1 - 1)²) = √(9 + 0) = √9 = 3
AC = √((0 - 3)² + (1 - 5)²) = √(9 + 16) = √25 = 5
Now, let's add up the lengths of the three sides:
Perimeter = AB + BC + AC = 4 + 3 + 5 = 12
So, the perimeter of triangle ABC is 12 units.
To find the perimeter of a triangle, you need to calculate the distance between each pair of vertices and then sum them up.
Step 1: Calculate the distance between points A(3,5) and B(3,1).
- The x-coordinate of both points is the same (3).
- To find the difference in y-coordinates, subtract the y-coordinate of point B from the y-coordinate of point A: 5 - 1 = 4.
- Hence, the distance between A and B is the absolute value of the difference in y-coordinates: |4| = 4.
Step 2: Calculate the distance between points B(3,1) and C(0,1).
- The y-coordinate of both points is the same (1).
- To find the difference in x-coordinates, subtract the x-coordinate of point C from the x-coordinate of point B: 3 - 0 = 3.
- Hence, the distance between B and C is the absolute value of the difference in x-coordinates: |3| = 3.
Step 3: Calculate the distance between points C(0,1) and A(3,5).
- To find the difference in x-coordinates, subtract the x-coordinate of point A from the x-coordinate of point C: 3 - 0 = 3.
- To find the difference in y-coordinates, subtract the y-coordinate of point C from the y-coordinate of point A: 5 - 1 = 4.
- Hence, the distance between C and A is the square root of the sum of the squares of the differences in x and y-coordinates: √(3^2 + 4^2) = √(9 + 16) = √25 = 5.
Step 4: Add up the distances to find the perimeter.
- Perimeter = Distance between A and B + Distance between B and C + Distance between C and A.
- Perimeter = 4 + 3 + 5 = 12.
Therefore, the perimeter of triangle ABC is 12 units.
To find the perimeter of a triangle, you need to calculate the sum of all three sides.
Step 1: Find the distance between points A(3, 5) and B(3, 1) using the distance formula.
The distance formula is given by:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
Using the distance formula, we can calculate the distance between A and B:
dAB = √[(3 - 3)^2 + (1 - 5)^2]
= √[0 + (-4)^2]
= √(0 + 16)
= √16
= 4
Step 2: Find the distance between points B(3, 1) and C(0, 1) using the distance formula.
Using the distance formula, we can calculate the distance between B and C:
dBC = √[(0 - 3)^2 + (1 - 1)^2]
= √[(-3)^2 + 0]
= √(9 + 0)
= √9
= 3
Step 3: Find the distance between points C(0, 1) and A(3, 5) using the distance formula.
Using the distance formula, we can calculate the distance between C and A:
dCA = √[(3 - 0)^2 + (5 - 1)^2]
= √[3^2 + 4^2]
= √(9 + 16)
= √25
= 5
Step 4: Add the distances to find the perimeter.
Perimeter = dAB + dBC + dCA
= 4 + 3 + 5
= 12
Therefore, the perimeter of triangle ABC is 12 units.
the distance from A to B is 4
The distance from A to C is sqrt(3^2+4^2)=5
the distance from B to C is 3
your teacher is to easy. Add the sides.