A coordinates (-8,-2)
B coordinates (6,19)
Find P so that the relation of the lenght of AP to the lenght of PB is 2 to 5
The distance between A and B in x is: 6 - (-8) = 6 + 8 = 14
The distance between A and B in y is: 19 - (-2) = 19 + 2 = 21
Since whe have to divide the segment AB in 7 equal segments (to put point P to distance of 2 to A and a dictance of 5 to B)
Each of the 7 seven segments will have an increment in x of 14/7 = 2
Each of the 7 seven segments will have an increment in y of 21/7 = 3
The x for the point P is the x of the point A plus 2 of our segments:
-8 + 2(2) = -8 + 4 = -4
The y for the point P is the y of the point A plus 3 of our segments:
-2 + 3(2) = -2 + 6 = 4
So the point P is at (-4, 4)
Answer:
P(-4, 4)
Distance between A and P in x: -4 - (-8) = -4 + 8 = 4
Distance between A and P in y: 4 - (-2) = 4 + 2 = 6
Distance between P and B is x: 6 - (-4) = 6 + 4 = 10
Distance between P and B in y: 19 - (4) = 15
You can see that the realtion between the distances is 2 to 5:
In x, AP distance is 4 and PB distance is 10, 4/10 = 2/5
In y, AP distance is 6 and PB distance is 15, 6/15 = 2/5