Please Help!!!

Question

Find the points
P1(x1, y1), P2(x2, y2), and P3(x3, y3)
on the line segment joining
A(6, 8) and B(9, 3)
that divide the line segment into four equal parts. (The points on the line are ordered
A, P1, P2, P3, and B.)

Answer 1

This can be easy.  First, find coordinates of midpoint of segment AB. Then you have M, whose coordinates are (15/2, 11/2), i.e. the x coordinate of M is the AVERAGE of the x coordinates of the endpoints, etc.

 

Next, Find midpoint of AM by the usual process(averaging these endpoints).

Finally, Find midpoint of MB.

 

You now have the three desired points.

Answer 2

Hello Rebecca.

 

This is one of those problems where it helps to draw a picture.

You can make a triangle by connecting the points A(6,8), B(9,3), and (6,3).

 

Imagine that you are starting from point A and moving along the diagonal to point B.

 

P1 is 1/4 of the way, P2 is 2/4 or 1/2 of the way, and P3 is 3/4 of the way from A to B.

 

P1(x1,y1) = A(6,8) + 1/4 * [B(9,3) - A(6,8)].

You can consider the x and y coordinates separately,

so let's solve for x1 and y1 one at a time.

 

x1 = 6 + 1/4 * (9-6) = 6 3/4 = 27/4. (Just look at the x coordinates)

y1 = 8 + 1/4 * (3-8) = 27/4.             (just look at the y coordinates)

 

So P1(x1,y1) = (27/4,27/4).

 

P2(x2,y2) = A(6,8) + 1/2 * [B(9,3) - A(6,8)].

x2 = 6 + 1/2 * (9-6) = 7 1/2 = 15/2.

y2 = 8 + 1/2 * (3-8) = 11/2.

 

P2(x2,y2) = (15/2,11/2).

 

P3(x3,y3) = A(6,8) + 3/4 * [B(9,3) - A(6,8)].

x3 = 6 + 3/4 * (9-6) = 33/4.

y3 = 8 + 3/4 * (3-8) = 17/4.

 

P3(x3,y3) = (33/4,17/4).

 

I hope this helps.

 

-Andrew M