If A and B are (-2,-2) and (2,-4) respectively find thr coordinates of P such that AP=3/7 AB and P lies on the line segment AB
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➩Given:-
- A line segment joining the points A(-2, -2) and B(2, -4)
- P is a point on AB such that AP = 3/7 AB
➩To Find:-
- Coordinates of P = ?
➩Solution:-
▶AP = 3/7 AB _[Given ]
▶7AP = 3 (AP + BP)
▶7AP = 3(AP) + 3(BP)
▶7AP - 3AP = 3BP
▶AP/BP = 3/4
Therefore point P divides AB internally in the ratio 3:4 !
✫ As we know that if a point ( h,k )
divides a line joining the point
(x1, y1 ) and (x2, y2) in the ratio m:n
then the coordinates of points are
given as
✫ (h,k) = (mx2+nx1/m+n,my2+ny1/
m+n
Where:
▶x1 = (-2) x2 = 2
▶y1 = (-2) y2 = (-4)
▶m : n = 3 : 4
▶Substituting the values, The coordinates of P
= { [3×(2)+ 4×(-2) / 3+4 ], [3×(-4)+4×(-2) / 3+4 ] }
= (-2/7, -20/7 )
Hence the coordinates of P are
(-2/7, -20/7 ) !
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