In a positive fraction, the denominator is greater than the numerator by $3.$ If $1$ is subtracted from both the numerator and the denominator, the fraction is decreased by $\frac{1}{14}.$ Find the fraction.

A straight line passes through the points $\mathrm{A}(-5, 2)$ and $\mathrm{B}(3, -6).$ It intersects the co-ordinate axes at points $\mathrm{C}$ and $\mathrm{D}$ as shown in the given diagram. $\mathrm{M}$ is a point on $\mathrm{AB}$ which divides $\mathrm{CD}$ in the ratio $1:2.$ Find:

The equation of $\mathrm{AB}.$

A straight line passes through the points $\mathrm{A}(-5, 2)$ and $\mathrm{B}(3, -6).$ It intersects the co-ordinate axes at points $\mathrm{C}$ and $\mathrm{D}$ as shown in the given diagram. $\mathrm{M}$ is a point on $\mathrm{AB}$ which divides $\mathrm{CD}$ in the ratio $1 : 2.$ Find:

The coordinates of points $\mathrm{C}$ and $\mathrm{D}$.

A straight line passes through the points $\mathrm{A}(-5, 2)$ and $\mathrm{B}(3, -6).$ It intersects the co-ordinate axes at points $\mathrm{C}$ and $\mathrm{D}$ as shown in the given diagram. $\mathrm{M}$ is a point on $\mathrm{AB}$ which divides $\mathrm{CD}$ in the ratio $1 : 2.$ Find:

the co-ordinates of point $\mathrm{M}.$
 

If $\frac{7\mathrm{a}+8\mathrm{b}}{7\mathrm{c}+8\mathrm{d}}=\frac{7\mathrm{a}-8\mathrm{b}}{7\mathrm{c}-8\mathrm{d}},$ prove that:

$\left(\mathrm{i}\right) \mathrm{a}:\mathrm{b} = \mathrm{c}:\mathrm{d}$       $\left(\mathrm{ii}\right) \frac{4\mathrm{a}-5\mathrm{b}}{4\mathrm{c}-5\mathrm{d}}=\frac{3\mathrm{a}+4\mathrm{b}}{3\mathrm{c}+4\mathrm{d}}.$

Calculate the ratio in which the line joining $\mathrm{A}(5, 6)$ and $\mathrm{B}(-3, 4)$ is divided by $x= 2.$ Also, find the point of intersection.