Find the perimeter of the triangle with vertices at A (0, 0), B (-4, -3) and C (-5, 0). If it is not possible, write “not possible” and explain why it is not possible.
A to B = sqrt(16+9 ) = 5
B to C = sqrt (1+9) = sqrt(10)
C to A = 5
so 10+sqrt(10)
To find the perimeter of a triangle, we need to calculate the distance between its vertices.
Let's start by finding the distance between points A (0, 0) and B (-4, -3).
The distance formula between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the distance AB:
d_AB = sqrt((-4 - 0)^2 + (-3 - 0)^2)
= sqrt((-4)^2 + (-3)^2)
= sqrt(16 + 9)
= sqrt(25)
= 5
Next, let's find the distance between points B (-4, -3) and C (-5, 0).
Using the same distance formula:
d_BC = sqrt((-5 - (-4))^2 + (0 - (-3))^2)
= sqrt((-5 + 4)^2 + (0 + 3)^2)
= sqrt((-1)^2 + (3)^2)
= sqrt(1 + 9)
= sqrt(10)
Lastly, let's find the distance between points C (-5, 0) and A (0, 0).
Using the distance formula again:
d_CA = sqrt((0 - (-5))^2 + (0 - 0)^2)
= sqrt((0 + 5)^2 + 0^2)
= sqrt((5)^2 + 0)
= sqrt(25)
= 5
Now we can find the perimeter by adding up the distances:
Perimeter = d_AB + d_BC + d_CA
= 5 + sqrt(10) + 5
= 10 + sqrt(10)
Therefore, the perimeter of the triangle with vertices A (0, 0), B (-4, -3), and C (-5, 0) is 10 + sqrt(10).
Note: It is always possible to find the perimeter of a triangle as long as we have the coordinates of its vertices.