Question

А(5;-4), В(-1;4),С(5;4) периметр трикутника?

Answer 1

Вектор АВ{Xb-Xa; Yb-Ya} = {-6;8}.  Модуль |AB|=√((-6)²+8²) = 10.

Вектор ВС{6;0}, |BC|=√(36+0) = 6.

Вектор АС{0;8}, |AC|=√(0+64} = 8.

Периметр Р= АВ+ВС+АС = 10+6+8 = 24 ед.

Answer 2

To find the perimeter of the triangle with vertices A(5, -4), B(-1, 4), and C(5, 4), we need to calculate the sum of the lengths of its three sides.

The distance formula between two points (x1, y1) and (x2, y2) in a 2D Cartesian coordinate system is given by:

Distance = √[(x2 - x1)^2 + (y2 - y1)^2]

Let's calculate the distances between the three pairs of points:

1. Distance between A and B: Distance_AB = √[(-1 - 5)^2 + (4 - (-4))^2] = √[(-6)^2 + (8)^2] = √[36 + 64] = √100 = 10

2. Distance between B and C: Distance_BC = √[(5 - (-1))^2 + (4 - 4)^2] = √[(5 + 1)^2 + 0] = √[6^2] = √36 = 6

3. Distance between C and A: Distance_CA = √[(5 - 5)^2 + (4 - (-4))^2] = √[0 + 8^2] = √64 = 8

Now, we sum up the three distances to find the perimeter:

Perimeter = Distance_AB + Distance_BC + Distance_CA = 10 + 6 + 8 = 24

So, the perimeter of the triangle with vertices A(5, -4), B(-1, 4), and C(5, 4) is 24 units.