Final answer:
To find a point four times farther from B towards A, calculate the differences in x and y coordinates from B to A, multiply them by 4, then add the results to B's coordinates to find the new point, which is (-52, -43).
Step-by-step explanation:
To find a point that is 4/1 or four times farther from point B (12, 5) to point A (-4, -7), we need to use the concept of partitioning a line segment in a given ratio. In this case, we want to find a point that divides the segment AB in the ratio of 4:1. First, we calculate the change in the x-coordinate and the y-coordinate (dx and dy) from B to A.
dx = Ax - Bx = (-4) - (12) = -16
dy = Ay - By = (-7) - (5) = -12
To find a point four times farther from B towards A, multiply dx and dy by 4:
- 4 * dx = 4 * (-16) = -64
- 4 * dy = 4 * (-12) = -48
Add these values to the coordinates of B to find the new point:
- New x-coordinate: Bx + 4 * dx = 12 + (-64) = -52
- New y-coordinate: By + 4 * dy = 5 + (-48) = -43
The new point is (-52, -43).