Find the perimeter of the triangle whose vertices are the following specified points in the plane? (0,-3), (-2,1) and (-4,6)
To find the distance between two points (x1, y1) and (x2, y2), all that you need to do is use the coordinates of these ordered pairs and apply the formula:
Distance = √((x2 − x1)^2 + (y2 − y1)^2)
So, in using this formula, we find that:
1. The distance between (0, -3) & (-2, 1) is √(20)
2. The distance between (-2, 1) & (-4, 6) is √(29)
3. The distance between (0, -3) & (-4, 6) is √(97)
Thus, the perimeter is the sum of these three distances.
√(20) + √(29) + √(97) = roughly 19.706
To find the perimeter of the triangle with the given vertices, you need to calculate the length of each side of the triangle and then add them together.
Step 1: Calculate the distance between (0, -3) and (-2, 1).
- The distance formula is given by: √[(x2 - x1)^2 + (y2 - y1)^2]
- Plugging in the coordinates, we get: √[(-2 - 0)^2 + (1 - (-3))^2] = √[(-2)^2 + (1 + 3)^2]
- Simplifying further: √[4 + 16] = √20
Step 2: Calculate the distance between (-2, 1) and (-4, 6).
- Using the distance formula: √[(-4 - (-2))^2 + (6 - 1)^2] = √[(-4 + 2)^2 + (6 - 1)^2]
- Simplifying further: √[(-2)^2 + (5)^2] = √[4 + 25] = √29
Step 3: Calculate the distance between (-4, 6) and (0, -3).
- Using the distance formula: √[(0 - (-4))^2 + (-3 - 6)^2] = √[(4)^2 + (-9)^2] = √[16 + 81] = √97
Step 4: Add the three side lengths together to get the perimeter.
- Perimeter = √20 + √29 + √97
Therefore, the perimeter of the triangle is √20 + √29 + √97 (units).
To find the perimeter of the triangle whose vertices are (-3,0), (1,-2), and (6,-4), we can use the distance formula.
The distance formula, also known as the Euclidean distance formula, calculates the distance between two points (x1, y1) and (x2, y2) in a two-dimensional Cartesian plane. The formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can calculate the distance between each pair of vertices and then sum those distances to find the perimeter.
Let's calculate the distances:
Distance between (-3,0) and (1,-2):
d1 = sqrt((1 - (-3))^2 + (-2 - 0)^2)
= sqrt(4^2 + (-2)^2)
= sqrt(16 + 4)
= sqrt(20)
= 2sqrt(5)
Distance between (-3,0) and (6,-4):
d2 = sqrt((6 - (-3))^2 + (-4 - 0)^2)
= sqrt(9^2 + (-4)^2)
= sqrt(81 + 16)
= sqrt(97)
Distance between (1,-2) and (6,-4):
d3 = sqrt((6 - 1)^2 + (-4 - (-2))^2)
= sqrt(5^2 + (-2)^2)
= sqrt(25 + 4)
= sqrt(29)
Now, let's sum the distances to find the perimeter:
Perimeter = d1 + d2 + d3
= 2sqrt(5) + sqrt(97) + sqrt(29)
Therefore, the perimeter of the triangle with vertices (-3,0), (1,-2), and (6,-4) is 2sqrt(5) + sqrt(97) + sqrt(29).