find the coordinates of point P on the line segment joining A(1,2) and B(6,7) such that AP= 2/5 AB - Maths - Coordinate Geometry

Question

find the coordinates of point P on the line segment joining A(1,2)
and B(6,7) such that AP= 2/5 AB

Shruti Tyagi · Accepted Answer

Dear Student,

Let the point P(x,y) divides the line joining point A(1,2) and B(6,7) in the ratio of m1 and m2
therefore x=m1x2+m2x1m1+m2 and y=m1y2+m2y1m1+m2putting values we getx=m1×6+m2×1m1+m2 and y=m1×7+m2×2m1+m2as we know APAB=25APAP+PB=22+3hence APPB=23=m1m2thus x=2×6+3×12+3 and y=2×7+3×22+3x=155 and y=205hence P(x,y)=3,4

Regards,