Question

Find the ratio in which point T(_1,6) divides the line segment joining the points p(_3,10) and Q(6,_8).

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Answer 1

Using the section formula, if a point (x,y) divides the line joining the points (x1,y1) and (x2,y2) in the ratio m:n, then 

(x,y)=(m+nmx2+nx1,m+nmy2+ny1)

Let the required ratio be m:n

A(−6,10)=(x1,y1) and B(3,−8)=(x2,y2)

we have,

(m+nmx2+nx1,m+nmy2+ny1)=(−4,6)

⇒m+nmx2+nx1=−4

⇒m(3)+n(−6)=−4m−4n

⇒3m−6n=−4m−4n

⇒3m+4m=6n−4n

⇒7m=2n

⇒nm=72

⇒m:n=2:7

Answer 2

Step-by-step explanation:

Let

SI/TR =R/1

From section's formula,

−1= 6R−3/RH

⇒6R−3=−R−1

⇒7R=2

⇒R=2/7

⇒ ST/TR =2/7

⇒ T divides SR is 2:7 ratio.

hope it is helpful