# 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 .

Dear Student!

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

Coordinates of

Coordinates of

Thus, the values of p and q are and 0 respectively.

Cheers!

• 99

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)

now see:

AP/PB =1/3

BY APPLYING SECTION FORMULA : 3*3+1*1/3+1 = 10/4 = 5/2 (FOR X COORDINATE) IE P

HENCE p=5/2

SIMILARLY PQ=BQ

THEREFORE FOR Y COORDINATE : -2*1+2*1/2=q

HENCE q=0

• -11
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