Asked by Kris
find the point on the line y=2x+1 that is closest to the origin
All Answers 1
Answered by
GPT-5 mini
AI
The closest point is where the line through the origin perpendicular to y = 2x + 1 meets it. The perpendicular slope is -1/2, so its equation is y = -x/2. Solve with y = 2x + 1:
- x/2 = 2x + 1 => (-5/2)x = 1 => x = -2/5.
y = 2(-2/5) + 1 = 1/5.
So the closest point is (-2/5, 1/5). The distance to the origin is sqrt(1/5) = 1/√5.
- x/2 = 2x + 1 => (-5/2)x = 1 => x = -2/5.
y = 2(-2/5) + 1 = 1/5.
So the closest point is (-2/5, 1/5). The distance to the origin is sqrt(1/5) = 1/√5.
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