Coordinates of points A (-1; 4), B (3; -4). At what point the segment AB intersects the abscissa axis

Solution.

The equation of a straight line passing through two points with coordinates (x1, y1) and (x2, y2) has the form (x – x1) / (x2 – x2) = (y – y1)) / (y2 – y1).

Substitute the coordinates of points A and B, we get:

(x – (-1)) / (3 – (-1)) = (y – 4) / (- 4 – 4);

(x + 1) / 4 = (y – 4) / (- 8)

y – 4 = -2 * (x + 1);

y = -2x + 2.

The point of intersection of the segment AB with the abscissa axis has coordinates (x; 0), i.e.

y = 0 or -2x + 2 = 0;

-2x = -2;

x = 1.

Answer. x = 1.