Question

If A(2, 2) and B(14, 10) find the point that will divide AB into a ratio of 3:1 starting from point A.

Answer 1

Answer:

Point $(11,8)$ divides $AB$ into a ratio of $3:1$ .

Step-by-step explanation:

Given: Points are $A(2,2)\,,\,B(14,10)$

To find: point that will divide $AB$ into a ratio of $3:1$ starting from point $A$.

Solution:

If the point $(x,y)$ divides the line joining points $A(u,v)$ and $B(p,q)$ in ratio $m:n$ then

$(x,y)=(\frac{mp+nu}{m+n},\frac{mq+nv}{m+n} )$

Put $(u,v)=(2,2)\,,\,(p,q)=(14,10)\,,\,m:n=3:1$

Therefore,

$(x,y)=(\frac{3(14)+1(2)}{3+1} ,\frac{3(10)+1(2)}{3+1} )=(\frac{42+2}{4},\frac{30+2}{4})=(\frac{44}{4},\frac{32}{4})=(11,8)$

Therefore,

point $(11,8)$ divides $AB$ into a ratio of $3:1$ .