The vertices of triangle ABC have coordinates: A (-2; 2), B (1; 4), C (0; 0). Make up the equations

The vertices of triangle ABC have coordinates: A (-2; 2), B (1; 4), C (0; 0). Make up the equations: 1) sides; 2) the medians of this triangle.

1. To solve the problem, we use the equation of a straight line passing through two points:
(x – x1) / (x2 – x1) = (y – y1) / (y2 – y1), where A (x1; y1), B (x2; y2).
Let’s write the equation for each side of the triangle:
AB.
(x – 1) / (-2 – 1) = (y – 4) / (2 – 4);
(x – 1) / -3 = y – 4 / -2
-2x + 2 = -3y + 12
3y – 2x – 10 = 0.
Sun.
(x – 0) / (1 – 0) = (y – 0) / (4 – 0);
x = y / 4, y = 4x.
AC.
(x – 0) / (-2 – 0) = (y – 0) / (2 – 0);
x / -2 = y / 2, y = -x.
2. The formula for the coordinates of the midpoint of the segment: (x1 + x2) / 2; (y1 + y2) / 2.
Point K is the middle of AB, let’s write down its coordinates. K (-0.5; 3).
Point N is the middle of the AC, its coordinates are (-1; 1).
Point M is the middle of the BC, its coordinates are (0.5; 2).
We do everything in the same way as in the first part of the task and we get.
Equation for the median SC: y = -6x.
The median equation AM: y = 2.
Median equation BN: 2y – 3x – 5 = 0.