The triangle is given by the vertices A (7; -6) B (-2; -2) and C (1; 2) find the equation of the straight line AM
March 31, 2021 | education
| The triangle is given by the vertices A (7; -6) B (-2; -2) and C (1; 2) find the equation of the straight line AM parallel to the side BC.
We have points:
A (7; -6), B (-2; -2), C (1; 2).
First, let’s write the equation of the line BC.
The equation has the formula y = k * x + b. Substitute the coordinates of points B and C and solve the system:
-2 = -2 * k + b;
2 = k + b;
Subtract the first from the second equation:
k + 2 * k = 2 + 2;
3 * k = 4;
k = 4/3;
Since line AM is parallel to line BC, their slopes are equal.
Linear AM equations:
y = 4/3 * x + b;
Substitute the coordinates of point A:
-6 = 4/3 * 7 + b;
b = -6-28/3;
b = -46/3;
y = 4/3 * x – 46/3 is the equation of the line AM.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.