Find the point P along the directed line segment from point A(-8, -2) to point B(0, 6) that divides the segment in the ratio 3:1.

Question

Find the point P along the directed line segment from point A(-8, -2) to point B(0, 6) that divides the segment in the ratio 3:1.

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Answer 1

You may use the distance formula to find the length of AB, then take 3/4ths of that (note: ratio of 3:1 means length of 4), then find the x and y coordinates of point P.

OR

You may move 3/4ths of the x-distance from A to B, then 3/4ths of the y-distance from A to B.

Both the x-distance and the y-distance is 8, and 3/4th of 8 is 6.

That makes the coordinates of point P (-2,4).

See the diagram below:

Answer 2

1. You can use the difference in coordinates, then multiply by 1/3 to each (x and y value), this will give you the added amount to the original coordinate that will be 1/3 the way between the points
2. (x-x₁), (y - y₁) = (0- -8),(6- -2) = (8,8)
3. multiply each by 1/3 ratio: ((1/3)(8), (1/3)(8)) = 8/3,8/3, this is the add to the original coordinates
4. (-8 + 8/3), (-2 + 8/3) = (-16/3, 2/3)

I hope this helps!

Answer 3

The equation of the line through A and B has y intercept 6 and slope (6-2)/8 = 1/2

y=(1/2)x+6

a ratio of 3:1 means 3/4 the way up the line

take 3/4 of 8 = 6. add it to the x coordinate at A: 6-8= -2

take 3/4 of 4 = 3 add it to the y coordinate at A 2+3 = 5

the point P = (-2,5) cuts the line segment in a ratio of 3:1