Question

Find the coordinates of the point 3/10 of the way from A to B. The points given are A(-3,-5) , B(9,6)

Answer 1

`\displaystyle\\Answer:\ (-(3)/(13),-2(6)/(13) )`

Explanation:

`\displaystyle\\(3)/(10) =0.3\\\\(-3,-5)\ \ \ \ \ (9,6)\\\\\boxed {x=(x_1+\lambda x_2)/(1+\lambda) }\ \ \ \ \ \ \ \ \ \ \ \boxed {y=(y_1+\lambda y_2)/(1+\lambda) }\\\\x_1=-3\ \ \ \ \ x_2=9\ \ \ \ \ y_1=-5\ \ \ \ \ \ \ y_2=6\\\\x=(-3+0.3*9)/(1+0.3) \\\\x=(-3+2.7)/(1.3) \\\\x=(-0.3)/(1.3)\\\\ x=-(0.3*10)/(1.3*10)\\\\ x=-(3)/(13) \\\\`

`\displaystyle\\y=(-5+0.3*6)/(1+0.3) \\\\y=(-5+1.8)/(1.3) \\\\y=(-3.2)/(1.3) \\\\y=-(3.2*10)/(1.3*10) \\\\y=-(32)/(13) \\\\y=-2(6)/(13) \\`