Mark on the coordinate plane points A (0; -10), B (4; -2), C (-7; 6), D (3; 1), write down the coordinates

Mark on the coordinate plane points A (0; -10), B (4; -2), C (-7; 6), D (3; 1), write down the coordinates of the point of intersection of line AB and ray CD.

At the request of the task on the coordinate plane Oxy, mark the points A (0; -10), B (4; -2), C (-7; 6) and D (3; 1). Thus, the first requirement of the assignment was fulfilled.
The second requirement of the specification concerns the coordinates of the point of intersection of the straight line AB and the ray CD. The figure clearly shows that the point of intersection of line AB and ray CD is point M with coordinates (5; 0). Let us prove this fact analytically. For this purpose, using the equation of a straight line passing through two points, we compose the equations of straight lines AB and CD. For AB we have: (x – 0) / (4 – 0) = (y – (-10)) / ((-2) – (-10)) or x / 4 = (y + 10) / 8, whence y = 2 * x – 10. Similarly, for CD, we get: (x – (-7)) / (3 – (-7)) = (y – 6) / (1 – 6) or (x + 7) / 10 = (y – 6) / (-5), whence y = -0.5 * x + 2.5. Equating the right-hand sides of the obtained equations, we compose the equality 2 * x – 10 = -0.5 * x + 2.5, which makes it easy to determine the value of the abscissa of the intersection point M. We have: 2.5 * x = 12.5, whence x = 12.5: 2.5 = 5. Consequently, the ordinate of the point M is equal to y = 2 * 5 – 10 = 0. This is what was required to prove.