Question

Find the ratio in which the line segment joining the points
. (-3, 10) and (6, -৪) is divided by (-1 6)
(-1, 6) ​

Answer 1

hope this answer will be helpful...

Answer 2

Answer:

The ratio in which the line segment joining the points (-3,10) and (6, -8) divided by the point of (-1, 6) = $\frac{2}{7}$

Step-by-step explanation:

Let us take ($x_{1} , y_{1}$) to be (-3, 10) and ($x_{2}$ , $y_{2}$) to be (6,8).

Let us also take (x, y) to be (-1, 6) and thus let us take the point (-1, 6)  to divide the line segment joining the points (-3, 10) and (6, 8) in the ratio of m : n.

From the formula for division of a line segment we can write

$(\frac{nx_1 + mx_2}{m+n} , \frac{ny_1 + my_2}{m+n} ) = (\frac{(-3)n + 6m}{m+n} , \frac{10n + (-8)m}{m+n} ) = (-1, 6)$

Therefore equating for x co-ordinate on both sides of the equation we can say that (-3n +6m) = -1 × (m + n)   ⇒ -3n + 6m = -m - n

Therefore -2n = -7m

Therefore we can write $\frac{m}{n} = \frac{2}{7}$

We can check the above by equating for y co-ordinate on both sides of the equation we can say that (10n - 8m) = 6 × (m + n)   ⇒ 10n - 8m = 6m + 6n

Therefore 4n = 14m

Therefore we can write $\frac{m}{n} = \frac{2}{7}$

The ratio in which the line segment joining the points (-3,10) and (6, -8) divided by the point of (-1, 6) = $\frac{2}{7}$