Find the coordinates of a point P on the line segment joining AC 1, 2) and B(6, 7
such That AP = 2/5 AB marked in bracket
Answers
Step-by-step explanation:
Given:-
Given points are A(1,2) and B(6,7)
and AP = 2/5 AB
To find:-
Find the coordinates of a point P on the linesegment joining A and B Such that AP = 2/5 AB.
Solution:-
Given points are A(1,2) and B(6,7)
AP = 2/5 AB
=>AP/AB = 2/5
=>AP/(AP+PB)=2/5
On applying cross multiplication then
=>5AP = 2(AP+PB)
=>5AP = 2AP + 2PB
=>5AP-2AP = 2 PB
=>3AP = 2PB
=>3AP/PB = 2
=>AP/PB = 2/3
AP:PB = 2:3
Let (x1, y1)=(1,2)=>x1=1 and y1 = 2
(x2, y2)=(6,7)=>x2=6 and y2=7
The ratio m1:m2 = 2:3 =>m1 = 2 and m2 = 3
We know that
The coordinates of the point P which divides the linesegment joining the points (x1, y1) and (x2, y2) in the ratio m1:m2 internally is
[(m1x2+m2x1)/(m1+m2) , (m1y2+m2y1)/(m1+m2)]
Now On Substituting the value then
P(x,y)=[{2(6)+3(1)}/(2+3) ,{2(7)+3(2)}/(2+3)]
=>P(x,y)=[(12+3)/5 ,(14+6)/5]
=>P(x,y)=(15/5 ,20/5)
P(x,y)=(3,4)
Answer:-
The coordinates of the point P=(3,4)
Used formula:-
The coordinates of the point P which divides the linesegment joining the points (x1, y1) and (x2, y2) in the ratio m1:m2 internally is
[(m1x2+m2x1)/(m1+m2) , (m1y2+m2y1)/(m1+m2)]
