Find by the coordinates of the vertices of the triangle ABC: 1) the perimeter of the triangle;

Find by the coordinates of the vertices of the triangle ABC: 1) the perimeter of the triangle; 2) equations of sides AB and BC. A (-1; 1); B (5; 1); C (3; 7).

We find the length of the side AB:
| AB | = √ ((- 1 – 5) ² + (1 – 1) ²) = √ ((- 6) ² + (0) ²) = √36 = 6.
Find the length of the BC side:
| Sun | = √ ((5 – 3) ² + (1 – 7) ²) = √ ((2) ² + (-6) ²) = √ (4 + 36) = √40 = 2√10.
Find the length of the speaker side:
| AU | = √ ((- 1 – 3) ² + (1 – 7) ²) = √ ((- 4) ² + (-6) ²) = √ (16 + 36) = √52 = 2√13.
We find the perimeter of the triangle ABC:
| AB | + | Sun | + | AC | = 6 + 2√10 + 2√13.
We write the equation of the side AB:
(x – (-1)) * (1 -1) = (y – 1) * (5 – (-1));
0 = (y – 1) * 6;
y = 1.
We write down the equation of the BC side:
(x – 5) / (3 – 5) = (y – 1) / (7 – 1);
(x – 5) / (-2) = (y – 1) / 6;
6 * (x – 5) / (-2) = y – 1;
(-3) * (x – 5) = y – 1;
-3x + 15 = y – 1;
y = -3x + 16.