Final answer:
The point F(-5, -9) translated by <4, 6> and then by <3, 5> has a final image at coordinates (2, 2).
Step-by-step explanation:
The student is asking about the result of performing two sequential translations on a point in the coordinate plane. Specifically, they want to determine the final coordinates of a point F after it is first translated by a vector <4, 6> and then by a second vector <3, 5>.
Translation of a point in the coordinate plane involves adding the components of the translation vector to the corresponding components of the point's coordinates. To find the image of point F which is initially at (-5, -9), the first translation along vector <4, 6> moves it to a new location. The new x-coordinate is found by adding the x-component of the translation vector to the x-coordinate of the point, and similarly for the y-coordinate:
The result is a new point at coordinates (-1, -3). Next, we perform the second translation using the vector <3, 5>:
Therefore, the final image of point F after both translations is at coordinates (2, 2).