Question

. Find the ratio in which (-1, -8)
divides the line segmen
joining te points (1-2)
(4,7)​

Answer 1

Step-by-step explanation:

Given that:

Find the ratio in which (-1, -8) divides the line segment joining the points (1-2) (4,7)

To find: Ratio

Solution: Let the C(-1,-8) ,A(1,-2) and B(4,7)

Let the point C divides the line segment joining A to B in m:n

Section Formula(Internal Division):

Coordinates of point of intersection

$x = \frac{mx_2 + nx_1}{m + n} \\ \\ y = \frac{my_2 + ny_1}{m + n}$

Put the values

$- 1 = \frac{4m + n}{m + n} \\ \\ - m - n = 4m + n \\ \\ - 4m - m = n + n \\ \\ - 5m = 2n \\ \\ \bold{\frac{m}{n} = \frac{ - 2}{5}}$

Ratio can never be negative.It shows that point C externally divides the line segment AB. So, apply

Section formula (Externally Division):

$x = \frac{mx_2 - nx_1}{m - n} \\ \\y = \frac{my_2 - ny_1}{m - n}\\ \\ - 1 = \frac{4m - n}{m - n} \\ \\ - m + n = - n \\ \\ - 5m = - 2n \\ \\ \bold{ \frac{m}{n} = \frac{2}{5}}$

Thus,

Point C(-1,-8) externally divides the line segment joining the points AB in 2:5.

Hope it helps you.

Answer 2

Answer:

Point C(-1,-8) externally divides the line segment joining the points AB in 2:5.

Point C(-1,-8) externally divides the line segment joining the points AB in 2:5.Hope it helps you..