In which quarter is the intersection point of the segments BN and MD, if B (-6; -3), N (6; 2), M (-4; 2), D (1; -4)?

The equation of a straight line passing through given points has the form

(y – y1) / (y2 – y1) = (x – x1) / (x2 – x1).

A straight line passes through points B (-6; -3), N (6; 2)

(y – (-3)) / (2 – (-3)) = (x – (-6)) / (6 – (-6));

y = 5/12 x – 6.

Through M (-4; 2), D (1; -4) –

(y – 2) / (-4 – 2) = (x – (-4)) / (1 – (-4));

y = -6/5 x – 14.

The intersection point of the segments BN and MD is calculated as the root of the system of equations

y = 5/12 x – 6 and

y = -6/5 x – 14.

x = – 4 92/97 and

y = -8 6/97.

The intersection point is in the third quarter of the coordinate plane.