Final answer:
The coordinates of point Y are found using the section formula, which gives us (-6, -5) when applying the ratio of XY to XZ as 3:4. This corresponds to option A: (-6, -5).
Step-by-step explanation:
To find the coordinates of point Y on line segment XZ given X(-9, -14) and Z(-5, -2) with XY to XZ in the ratio 3:4, we can use the section formula, which is a formula for internal division of a line segment by a given ratio.
Let's first calculate the distance between the given points X and Z by finding the differences in their x-coordinates and y-coordinates:
- Difference in x: (-5) - (-9) = 4
- Difference in y: (-2) - (-14) = 12
The coordinates of Y can be found by dividing these differences by the total parts of the ratio (which is 3+4=7) and multiplying by the parts for XY, that is 3:
- Y's x coordinate: -9 + ((4/7) * 3) = -9 + (12/7) = -6
- Y's y coordinate: -14 + ((12/7) * 3) = -14 + (36/7) = -5
Therefore, the coordinates of point Y are (-6, -5), which corresponds to option A: (-6, -5).