Point P=(1,2) partitions the segment from E=(9,6) to F in a 2:5 ratio. Find the coordinates of point F.

Question

I need the working for this. Thanks.

Answer 1

Hello, Yousef,

I created the equation for a straight line through the two given points. Calculate the slope, m, by using the "Rise/Run" method. Then find "b" by solving for one of the given points. The equation I get is y = 0.5x+1.5.

I calculated the distance between P and E using the quadratic formula. Since this segment is 2/5 of the total, Divide it by (5/7) to get the length of the segment FP. Find the coordinates of x and y that produce that distance, using the quadratic formula again. I get (-20.5, -8.75).

Unfortunately, there isn't enough room here to add my graph.

Messy. I hope someone can describe a more straightforward approach.

Bob

Answer 2

9-1 = 8 = change in x

6-2 = 4 = change in y = half the change in x

d^2 = 64+16 = 80 = distance squared

d=sqr80 = 4sqr5 from P to E which is 2/7 of the distance from E to F = 14sqr5

from P to F = 14sq5-4sqr5 = 10sqr5

P to F has y change -10 and x change -20 (twice the change in y)

P(1,2) - (20,1) =

F (-19,-8)

Plot the points, E and P. Connect them with a straight line, extend the line down to the left, draw some right triangles and you get one triangle with base 8, height 4 hypotenuse 4sqr5 and a 2nd triangle base 20,height 10, hypotenuse 10sqr5

there is, however, a slight ambiguity in the problem as to whether EP is 2/7 or 5/7 of the full line

the above was solved treating EP as 2/7 of EF

If it were 5/7 then PF would be 2/7 of EF, with F (-2.6,-0.6)