Question

If a point $P\left(\frac{23}{5},\frac{33}{5}\right)$ divides line AB joining two points $A(3,5)$ and $B(x,y)$ internally in ratio of $2:3$, then the values of $x$ and $y$ will be.

• A. $x=4,y=7$
• B. $x=5,y=9$
• C. $x=7,y=9$
• D. $x=7,y=8$

Answer 1

Answer: (C)

$x=7,y=9$

Here we apply the section formula, i. e. if a point $P(a,b)$ divides the line segment $AB$ joining the points $A(x_1,y_1)\&B(x_2,y_2)$ in the ratio $m:n$ then we have

$a=\frac{n{x}_1+m{x}_2}{m+n}\&b=\frac{n{y}_1+m{y}_2}{m+n}.$

$\therefore$ $\frac{23}{5}=\frac{2\times x+3\times 3}{2+3}$ and $\frac{33}{5}=\frac{2\times y+3\times 5}{2+3}$

$\frac{23}{5}=\frac{2x+9}{5}$ and $\frac{33}{5}=\frac{2y+15}{5}$

$115=10x+45$ and $165=10y+75$

$x=\frac{70}{10}$ and $\frac{90}{10}$

$x=7$ and $y=9$.