Find the perimeter of the triangle whose vertices are the following specified points in the plane (-2,-7) (1,-6) and (-7,7)
I assume you know how to find the distance between two points.
I will do the first length, you do the rest.
from (-2,-7) to (1,-6)
distance = √( (-2-1)^2 + (-7+6)^2 )
= √( 9 + 1)
= √10
after finding the other two, add them up
fi
nd the perimeter of the triangle whose vertices are the following specified points in the plane.
(−10, −3), (7, 4)
and
(−1, 7)
To find the perimeter of a triangle, we need to calculate the sum of the lengths of all its sides.
The formula to find the distance between two points (x1, y1) and (x2, y2) in a plane is the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distances between the given points to find the lengths of the sides:
Side 1: (-2, -7) to (1, -6)
d1 = √((1 - (-2))^2 + (-6 - (-7))^2)
= √(3^2 + 1^2)
= √(9 + 1)
= √10
Side 2: (1, -6) to (-7, 7)
d2 = √((-7 - 1)^2 + (7 - (-6))^2)
= √((-8)^2 + (13)^2)
= √(64 + 169)
= √233
Side 3: (-7, 7) to (-2, -7)
d3 = √((-2 - (-7))^2 + (-7 - 7)^2)
= √(5^2 + 14^2)
= √(25 + 196)
= √221
Now, let's calculate the perimeter by adding the lengths of the sides:
perimeter = d1 + d2 + d3
= √10 + √233 + √221
So, the perimeter of the triangle with vertices (-2, -7), (1, -6), and (-7, 7) is approximately √10 + √233 + √221 units.