The coordinates of the vertices of the triangle are A (-2; 3), B (4; -2) and C (1; 5). Draw up equations of straight lines

The coordinates of the vertices of the triangle are A (-2; 3), B (4; -2) and C (1; 5). Draw up equations of straight lines passing through each of the vertices parallel to the opposite side.

The coordinates of the vertices of the triangle are A (-2; 3), B (4; -2) and C (1; 5).

a) Let us compose the equations of the straight line passing through point A parallel to the side BC.

Find the BC vector:

BC (1 – 4; 5 + 2) that is, BC (-3; 7)

The equation of a straight line passing through point A will be:

-3 * (x + 2) + 7 * (y – 3) = 0;

-3h + 7y – 27 = 0.

b) Let’s compose the equations of the straight line passing through point B parallel to the AC side.

Find the vector AC:

AC (1 + 2; 5 – 3) that is, AC (3; -2).

The equation of a straight line passing through point B will look like:

3 * (x – 4) – 2 * (y + 2) = 0;

3x – 12 -2y – 4 = 0;

3x – 2y – 16 = 0.

c) We compose the equations of the straight line passing through the point C parallel to the side AB.

Find the vector AB:

AB (6; -5).

The equation of a straight line passing through point C will look like:

6 * (x – 1) – 5 * (y – 5) = 0;

6x – 6 – 5y + 25 = 0;

6x – 5y + 19 = 0.