Question

P And w are the points with coordinates (2,-1) and (3,-4) respectively.find the coordinates of the point r such that pr is divided in the ratio 2/5 of pq

Answer 1

Answer:

R = ( 12 / 5,  -11 / 5 ) = ( 2.4, -2.2 )

Step-by-step explanation:

P = ( 2, -1 )

Q = ( 3, -4 )

The point that is proportion t of the way from P to Q is

( 1 - t ) P + t Q.

[ e.g. If t = 0, then "none of the way from P to Q" is P.

If t = 1, then "all the way from P to Q" is Q.  Etc. ]

As the question is worded, I suspect that what is wanted is for PR to be 2/5 of PQ.  So we want R that is t = 2/5 of the way from P to Q.  So...

R = (3/5) P + (2/5) Q

= (  (3×2 + 2×3) / 5 ,  (3×-1 + 2×-4) / 5 )

= ( (6+6) / 5,  (-3-8) / 5 )

= ( 12 / 5,  -11 / 5 )

= ( 2.4, -2.2 )