Question

What is the answer for this and why? Show work

Answer 1

Answer: (-4.5,-3)

Explanation:

(-9,-2) (9,-6) 1:3

`\displaystyle\\\boxed {x=(x_1+\lambda x_2)/(1+ \lambda) \ \ \ \ \ \ y=(y_1+\lambda y_2)/(1+\lambda) }`

`\displaystyle\\x_1=-9\ \ \ \ x_2=9\ \ \ \ \ y_1=-2\ \ \ \ \ \ y_2=-6\ \ \ \ \ \lambda=1:3=(1)/(3) \\\\x=(-9+((1)/(3))(9) )/(1+(1)/(3) ) \\\\x=(-9+3)/(((1)(3)+1)/(3) ) \\\\x=(-6)/((3+1)/(3) ) \\\\x=((-6)(3))/(4) \\\\x=(-18)/(4)\\\\x=-4.5 \\\\y=(-2+((1)/(3) )(-6))/(1+(1)/(3) ) \\\\y=(-2+(-2))/((4)/(3) ) \\\\y=((-4)(3))/(4) \\\\y=-3\\Thus,(-4.5,-3)`