Answer: The coordinates of M are ( 1,-7)
Step-by-step explanation:
Since we know that,
If a point intersects a line having the end points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] internally in the ration of m:n,
Then By section formula,
The coordinates of the points are, [tex]( \frac{m\times x_2+n\times x_1}{m+n} , \frac{m\times y_2+n\times y_1}{m+n} )[/tex]
Here, [tex]x_1 = -4, x_2 = 4, y_1= -2[/tex] and [tex]y_2 = -10[/tex]
While m = 5 and n =3
Therefore coordinates of M are, [tex]( \frac{5\times 4+3\times -4}{5+3} , \frac{5\times -10+3\times -2}{5+3} )[/tex]
= [tex]( \frac{20-12}{8} , \frac{-50-6}{8} )[/tex]
= [tex]( \frac{8}{8} , \frac{-56}{8} )[/tex]
= [tex](1, -7 )[/tex]
