Question

If a point P(k,7) divides the line segment joining A(8,9) and B(1,2) in a ratio m:n then find the values of m and n.

• A. m=5,n=2
• B. m=7,n=1
• C. m=2,n=5
• D. m=1,n=7

Answer 1

Answer:

C. m=2,n=5

$x_1=8,y_1=9,x_2=1,y_2=2,x=k,y=7$

$P(x,y)=(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

$(k,7)=(\frac{m \times 1 +n\times8}{m+n},\frac{m \times 2 +n \times 9}{m+n})$

$\frac{m \times2+n\times9}{m+n}=7$

$2m+9n=7m+7n$

$-5m=-2n$

$\frac{m}{n}=\frac{2}{5}$

$m=2,n=5$