Find the perimeter of the triangle whose vertices are the following specified points in the plane.
(−9,−6),(−3,−6) and (9,−4)
Plot tyhe points, and use the distance formula to find the sides.
For example, if the points are ABC, then
AB = √((-3+9)^2 + (-6+3)^2) = √(36+9) = √45
find the other two sides and add them up.
Or if, as I suspect C = (-9,-4), then you have a right triangle, and the legs are easy to find the lengths. Then just find the hypotenuse and add 'em up.
To find the perimeter of a triangle, we need to calculate the sum of the lengths of all three sides.
The distance between two points (x1, y1) and (x2, y2) in a plane can be found using the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distances between the given points:
Distance between (-9, -6) and (-3, -6):
x1 = -9, y1 = -6
x2 = -3, y2 = -6
Distance = sqrt((-3 - (-9))^2 + (-6 - (-6))^2)
= sqrt(6^2 + 0^2)
= sqrt(36 + 0)
= sqrt(36)
= 6
Distance between (-9, -6) and (9, -4):
x1 = -9, y1 = -6
x2 = 9, y2 = -4
Distance = sqrt((9 - (-9))^2 + (-4 - (-6))^2)
= sqrt(18^2 + 2^2)
= sqrt(324 + 4)
= sqrt(328)
Distance between (-3, -6) and (9, -4):
x1 = -3, y1 = -6
x2 = 9, y2 = -4
Distance = sqrt((9 - (-3))^2 + (-4 - (-6))^2)
= sqrt(12^2 + 2^2)
= sqrt(144 + 4)
= sqrt(148)
Now, we can calculate the perimeter by summing up the distances:
Perimeter = 6 + sqrt(328) + sqrt(148)
Note: Since the distances involve square roots, the precise value of the perimeter may result in an irrational number. If you prefer, you can use an approximation for the square roots to get a decimal approximation for the perimeter.