what point on the line y = 3x + 6 is closest to the origin? let d be the distance between the two points…

what point on the line y = 3x + 6 is closest to the origin? let d be the distance between the two points. what is the objective function in terms of the x - coordinate? d = (type an expression.)

what point on the line y = 3x + 6 is closest to the origin? let d be the distance between the two points. what is the objective function in terms of the x - coordinate? d = (type an expression.)

Answer

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $D=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, one - point is $(x,y)$ on the line $y = 3x+6$ and the other is the origin $(0,0)$. So $x_1 = 0,y_1 = 0,x_2=x,y_2=3x + 6$.

Step2: Substitute into distance formula

$D=\sqrt{(x - 0)^2+(3x + 6-0)^2}=\sqrt{x^{2}+(3x + 6)^{2}}=\sqrt{x^{2}+9x^{2}+36x + 36}=\sqrt{10x^{2}+36x + 36}$

Answer:

$\sqrt{10x^{2}+36x + 36}$