Final answer:
To find the y-coordinate of point C on segment AB, where C divides AB in the ratio 3:1, use the formula C(y) = (3 * yB + yA) / (3 + 1), where yA and yB are the y-coordinates of point A and B, respectively.
Step-by-step explanation:
The question is asking us to find the y-coordinate of point C which lies on the line segment AB in a given ratio. Given the lack of specific coordinates for A and B, we will use the information provided to give a general approach to solving such a problem. If the ratio of AC to CB is 3:1, then point C divides the segment AB into four equal parts. Point C is three parts from A and one part from B, based on the ratio provided.
The general formula to find a point that divides a segment in a given ratio is P(x,y) = ((m * x2 + n * x1) / (m + n), (m * y2 + n * y1) / (m + n)), where m:n is the given ratio, (x1, y1) are the coordinates of point A and (x2, y2) are the coordinates of point B. In this case, we substitute m with 3 and n with 1 to find the coordinates of point C.
To find the y-coordinate of point C: C(y) = (3 * yB + yA) / (3 + 1), where yA and yB are the y-coordinates of A and B, respectively. Adjust this formula with your specific points' coordinates to get your answer.