Final answer:
To find a point that is 7/10 of the way from point A (-4,-8) to point B (11,5), calculate the change in x and y from A to B, multiply these by 7/10, and add the results to point A's coordinates. The resulting coordinates are (6.5, 1.1).
Step-by-step explanation:
Finding Coordinates on a Line Segment
To find the coordinates of the point that is 7/10 of the way from point A to point B, you can use the following method:
Find the change in the x-coordinate (Δx) and the change in the y-coordinate (Δy) from point A to point B by subtracting the coordinates of A from the coordinates of B.
Δx = xB - xA = 11 - (-4) = 15
Δy = yB - yA = 5 - (-8) = 13
Multiply Δx and Δy by 7/10 to find how far the point has moved from A towards B in each direction.
The moved distance in the x direction: 15 * (7/10) = 10.5
The moved distance in the y direction: 13 * (7/10) = 9.1
Add these distances to the coordinates of point A to get the new point's coordinates.
New x coordinate: -4 + 10.5 = 6.5
New y coordinate: -8 + 9.1 = 1.1
The coordinates of the point 7/10 of the way from A to B are (6.5, 1.1).