Find the point on the line x + y − 2 = 0 that is closest to the point (-2, 5)
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What you want is the intersection of the line perpendicular to the given line which passes through the given point. Can you proceed?
So a line orthogonal to x + y - 2 = 0?
Originally Posted by biggerleaffan So a line orthogonal to x + y - 2 = 0? Note that $\displaystyle x-y+7=0$ is a line through $\displaystyle (-2,5)$ and perpendicular to the given line. Where do they intersect?
Originally Posted by Plato Note that $\displaystyle x-y+7=0$ is a line through $\displaystyle (-2,5)$ and perpendicular to the given line. Where do they intersect? -5/2, 9/2. Is this then the answer to my original question?
Originally Posted by biggerleaffan -5/2, 9/2. Is this then the answer to my original question? I don't know if that is correct. I will not do the algebra. But by definition: the distance from a point to a line is the length of the line segment from the point to the line.
Originally Posted by Plato I don't know if that is correct. I will not do the algebra. But by definition: the distance from a point to a line is the length of the line segment from the point to the line. There are many "line segments from the point to the line". By definition: the distance from a point to a line is the length of the line segment, perpendicular to given line, from the point to the line.
Originally Posted by HallsofIvy There are many "line segments from the point to the line". By definition: the distance from a point to a line is the length of the line segment, perpendicular to given line, from the point to the line. RIGHT! I have no idea where my "perpendicular" went to. Clearly a typo. Thank you.
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