Find the point on the line $y=4 x+8$ that is closest to the origin.
A) $\left(-\frac{31}{17}, \frac{8}{17}\right)$
B) $\left(-\frac{34}{17}, \frac{9}{17}\right)$
C) $\left(-\frac{32}{17}, \frac{10}{17}\right)$
D) $\left(-\frac{32}{17}, \frac{8}{17}\right)$
E) $\left(-2, \frac{8}{17}\right)$

Question

Quizplus · Accepted Answer

The point on the line closest to the origin is found by projecting the origin onto the line. The line perpendicular to $y=4x+8$ has a slope of $-\frac{1}{4}$. Solving the system of equations for the intersection gives the point $\left(-\frac{32}{17}, \frac{8}{17}\right)$.

Find the Point on the Line y=4x+8y=4 x+8y=4x+8 That Is Closest to the Origin

Find the Point on the Line $y=4 x+8$ That Is Closest to the Origin