Question

P and Q are the points with coordinates (2,-1 )and (-3,4 )find the coordinates of the point R such that PR is 2 / 5 of PQ.

Answer 1

R(0,1) Using Section Formula

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Answer 2

The coordinates of point R are (0,1)

1. The condition to be satisfied according to the question is PR=(2/5)PQ

2. Hence, we know that the ratio of PR:RQ= 2:3.

3. Assign the values of the ratio to m and n. Hence m=2, n=3

4. P=(x1,y1)=(2,-1) and Q=(x2,y2)=(-3,4)

5. Using Section Formula:

R={ (mx2 + nx1)/(m + n) , (my2 + ny1)/(m + n)}

= { [2(-3) + 3(2)] / [ 2 + 3] , [2(4) +3(-1)] / [ 2+ 3]}

={ (-6+6)/5, (8-3)/5)

=(0,1)