please helppppp

Question

Given the points, A (-4, 7) and B (8, 3), find the coordinates of the point P on the directed line segment AB¯¯¯¯¯¯¯¯AB¯that partitions AB¯¯¯¯¯¯¯¯AB¯ in the ratio 3:1.

P= ____

Answer 1

Hi Adrianna W.

P(5,4)

Just for clarity, I have a question, you want to know the coordinates of point P on the directed line segment AB based the ratio of the distances of A to P and P to B?

(AP)/(PB) = 3/1?

Where AP = The coordinates of P minus the coordinates of A.

x -(-4)

y-7

Where PB = The coordinates of B minus the coordinates of P

8-x

3-y

If so, then according to the ratio just plug in the values and solve for

The x coordinate

AP = 3(PB)

x + 4 = 3(8-x)

x+4 = 24 - 3x

x + 3x = 24 -4

4x = 20

x = 5

The y coordinate is calculated the same way

y-7 = 3(3-y)

y-7 = 9 -3y

y + 3y = 9 + 7

4y = 16

y = 4

The coordinates of P = (5,4)

Checking the ratio of the distances AP/PB

(5-(-4))/(8-5) = (5+4)/(3)= 9/3 = 3/1

You can check the ratio of the y distance in the same manner

While there are several other ways to do the problem if the question I asked above is true I hope this helps.

Answer 2

A(-4,7) and B(8.3) A to B

midpoint is the averages of x and y values: M(2,5)

midpoint of (-4,7) to (2,5) is 1/4 the way from A to B (-1,6)

and from (2,5) to (8,3) 3/4 the way from A to B (5,4)

(5,4) partitions AB in a 3:1 ratio

(-1,6) partitions AB in a 1:3 ratio