Triangle ABC has Coordinates A(-6,0) B(-2,0) C(-2,-7). What is the APPROXIMATE Perimeter of Triangle ABC?
if you look at the coordinates, you just have a right triangle, with legs of length 4 and 7. So, figure the hypotenuse and add 'em up. I get something close to 19.
Thank you Steve God bless you
To find the perimeter of a triangle, we need to find the length of each side and then add them up.
The length of a side is given by the distance formula, which is the square root of the sum of the squares of the differences in x-coordinates and y-coordinates.
Let's calculate the length of each side:
Side AB:
x-coordinates: -2 - (-6) = 4
y-coordinates: 0 - 0 = 0
Length AB = √(4^2 + 0^2) = √16 = 4
Side BC:
x-coordinates: -2 - (-2) = 0
y-coordinates: -7 - 0 = -7
Length BC = √(0^2 + (-7)^2) = √49 = 7
Side CA:
x-coordinates: -6 - (-2) = -4
y-coordinates: 0 - (-7) = 7
Length CA = √((-4)^2 + 7^2) = √(16+49) = √65 ≈ 8.06
Now, let's add up the lengths of all three sides to find the approximate perimeter of triangle ABC:
Perimeter = AB + BC + CA ≈ 4 + 7 + 8.06 ≈ 19.06
Therefore, the approximate perimeter of Triangle ABC is approximately 19.06 units.
To find the approximate perimeter of Triangle ABC, we need to calculate the distances between its vertices. Here's how we can do that:
1. Calculate the distance between points A and B using the distance formula:
distance AB = √((x2 - x1)^2 + (y2 - y1)^2)
For A(-6, 0) and B(-2, 0), the calculation becomes:
distance AB = √((-2 - (-6))^2 + (0 - 0)^2)
Simplifying further:
distance AB = √((4)^2 + (0)^2)
distance AB = √(16 + 0)
distance AB = √16
distance AB = 4
2. Calculate the distance between points B and C using the distance formula:
distance BC = √((x2 - x1)^2 + (y2 - y1)^2)
For B(-2, 0) and C(-2, -7), the calculation becomes:
distance BC = √((-2 - (-2))^2 + (-7 - 0)^2)
Simplifying further:
distance BC = √((0)^2 + (-7)^2)
distance BC = √(0 + 49)
distance BC = √49
distance BC = 7
3. Calculate the distance between points A and C using the distance formula:
distance AC = √((x2 - x1)^2 + (y2 - y1)^2)
For A(-6, 0) and C(-2, -7), the calculation becomes:
distance AC = √((-2 - (-6))^2 + (-7 - 0)^2)
Simplifying further:
distance AC = √((4)^2 + (-7)^2)
distance AC = √(16 + 49)
distance AC = √65 (approximated to two decimal places)
4. Finally, add up the calculated distances to find the approximate perimeter of Triangle ABC:
Perimeter ≈ distance AB + distance BC + distance AC
Perimeter ≈ 4 + 7 + √65 (approximated to two decimal places)
Hence, the approximate perimeter of Triangle ABC is approximately 4 + 7 + √65.