Question

The ratio in which the line segment joining the points P(-3, 10) and Q(6, – 8) is divided by O(-1, 6) is

Answer 1

Step-by-step explanation:

Given:The ratio in which the line segment joining the points P(-3, 10) and Q(6, – 8) is divided by O(-1, 6) is

To find:ratio of division

Solution:

We know that if point A(x1,y1) and B(x2,y2) point C(x,y) divides the joining of AB in m:n,then coordinates of C are

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

here

P(-3, 10) and Q(6, – 8) is divided by O(-1, 6)

Put the values in formula to find the ratio

$- 1 = \frac{6m - 3n}{m + n}$

Cross multiply and put the terms of m and n in separate sides

$- m - n = 6m - 3n \\ \\ - m - 6m = - 3n + n \\ \\ - 7m = - 2n \\ \\ 7m = 2n \\ \\ \frac{m}{n} = \frac{2}{7} \\ \\ \bold{m \ratio n = 2 \ratio 7}$

The ratio of division of line is 2:7

Hope it helps you.

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