# The Line Segment Joining the Points A(3,-4) and B(1,2) is Trisected at the Points P(P, -2) and Q (5/3,Q). . Find the Values of P and Q. - Mathematics

The line segment joining the points A(3,-4) and B(1,2) is trisected at the points P(p, -2) and Q (5/3,q). . Find the values of p and q.

#### Solution

Let P and Q be the points of trisection of AB.

Then, P divides AB in the radio 1:2

So, the coordinates of P are

 x= ((mx_2 +nx_1))/((m+n)) , y = ((my_2+ny_1))/((m+n))

 ⇒ x = ({ 1 xx 1+2xx(3)})/(1+2) , y = ({1 xx 2+2xx(-4)})/(1+2)

 ⇒ x = (1+6)/3 , y (2-8)/3

 ⇒ x = 7/3 , y -6/3

 ⇒x =7/3 , y =-2

Hence, the coordinates of P are (7/3 , -2)

But ,(p -2) are the coordinates of P.

so , p=7/3

Also, Q divides the line AB in the ratio 2:1

So, the coordinates of Q are

x = ((mx_2 +mx_1))/((m+n)) , y = ((my_2+my_1))/((m+n))

⇒x = ((2xx1+1xx3))/((2+1)) , y = ({ 2xx2+1xx(-4)})/(2+1)

⇒ x = (2+3)/3 , y = (4-4)/3

⇒ x = 5/3 , y =0

Hence, coordinates of Q are (5/3, 0)

But the given coordinates of Q are (5/3,q)

so , q=0

Thus , p=7/3 and q =0

Concept: Coordinate Geometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 7