Final answer:
To find the y-coordinate of point P that partitions AB in the ratio 1:3, first calculate the distance between A and B using the distance formula. Then, consider the difference in y-coordinates between A and B as the endpoints. Multiply this difference by 3 and add it to the y-coordinate of A to find the y-coordinate of point P.
Step-by-step explanation:
To find the y-coordinate of point P that partitions AB in the ratio 1:3, we first need to determine the distance from point A to point B. Using the distance formula, we have:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
d = sqrt((-5 - 5)^2 + (3 - (-1))^2)
d = sqrt((-10)^2 + (4)^2) = sqrt(100 + 16) = sqrt(116)
d = sqrt(4 * 29) = 2sqrt(29)
Since we want to find the y-coordinate of point P that partitions AB in the ratio 1:3, we can consider the y-coordinates of A and B as the endpoints of a line segment.
Using the ratio 1:3, we can calculate the difference of the y-coordinates:
3 - (-1) = 4
The difference between the y-coordinate of A and the y-coordinate of point P is 4 units. Since point P is 3 times farther from B than from A, we can multiply the difference by 3:
4 * 3 = 12
Finally, we can find the y-coordinate of point P by adding the result to the y-coordinate of A:
-1 + 12 = 11
Therefore, the y-coordinate of point P that partitions AB in the ratio 1:3 is 11.