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Find the point on the line $ y = 2x + 3 $ that is closest to the origin.

$$\left(-\frac{6}{5}, \frac{3}{5}\right)$$

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Oregon State University

University of Michigan - Ann Arbor

Idaho State University

Okay, let's use the distance formula. Shoe expose three. The minus zero doesn't affect the problem. Plus X minus zero squared is just plus X squared. This gives us the square root five X squared plus 12 ax plus nine. So now we have five x squared plus 12 ax plus nine equals. Why therefore wide prime is equivalent to 10 Expose 12. We're just taking the derivative. So that's equal to zero solve for acts and we get access equivalent to night of six divided by five. Which means that we have why equals two times negative six over five plus three, which is three divided by five. So we have negative 6/5 Karmah 3/5 or negative 1.2 comma 0.6