Question

what ratio does the point (x, 6)divides the line segment joining points A(-6,10),B(3,-8) and find the value of x​

Answer 1

Step-by-step explanation:

A(-6,10) & B(3,-8)

x = m1(3) + m2(-6) / m1 + m2

x(m1 + m2) = 3m1 - 6m2

(x - 3)m1 = -(x + 6)m2

m1/m2 = -(x + 6)/(x - 3) -------(1)

And

6 = m1(-8) + m2(10) / m1 + m2

6(m1 + m2) = -8m1 + 10m2

14m1 = 4m2

m1 / m2 = 4/14 = 2/7

Now ,

-(x + 6)/(x - 3) = 2/7

-7(x + 6) = 2(x - 3)

-7x - 42 = 2x - 6

-7x - 2x = -6 + 42

-9x = 36

x = 36/-9 = -4