- the line segment joining the points (3,-4)and (1,2)is trisected at the points Pand Q. if the coordinates of Pand Q are (p,-2) and (5/3,q) respectively, find the values of p and q .
Let the given point be A(3, – 4) and B(1, 2).
Given, P and Q trisects AB.
∴ AP = PQ = QB
Now, AP + PQ + QB = AB
∴ AP + AP + AP = AB
⇒ 3AP = AB
∴ P divides AB in the ratio 1 : 2
Similarly, Q divides AB in the ratio 2 : 1
Coordinates of the point dividing the line segment joining (x1, y1) and (x2, y2) is the ratio m : n is
Thus, the values of p and q are and 0 respectively.
to understand my solution please take apen and and a paper and do the following:
draw a line segment AB and trisect it by P &Q. (the order should be APQB)
BY APPLYING SECTION FORMULA : 3*3+1*1/3+1 = 10/4 = 5/2 (FOR X COORDINATE) IE P
THEREFORE FOR Y COORDINATE : -2*1+2*1/2=q