document.write( "Question 978141: the line y=2x+7 is parallel to the line y=2x-3.The line y= -0.5x+7 is perpendicular to the line y=2x-3. Find the perpendicular distance between the pair of parallel lines. \n" ); document.write( "

Algebra.Com's Answer #599708 by KMST(5328) $\"\"$ $\"About$

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Line $\"blue%28y=2x-3%29\"$ is parallel to line $\"red%28y=2x%2B7%29\"$ ,
\n" ); document.write( "which is perpendicular to $\"green%28y=-0.5x%2B7%29\"$ ,
\n" ); document.write( "so $\"blue%28y=2x-3%29\"$ and $\"green%28y=-0.5x%2B7%29\"$ are perpendicular to each other.
\n" ); document.write( "So the distance between $\"blue%28y=2x-3%29\"$ and $\"red%28y=2x%2B7%29\"$
\n" ); document.write( "is the distance, along $\"green%28y=-0.5x%2B7%29\"$ ,
\n" ); document.write( "between the points where $\"green%28y=-0.5x%2B7%29\"$ intersects the other two lines.
\n" ); document.write( "Lines $\"green%28y=-0.5x%2B7%29\"$ and $\"red%28y=2x%2B7%29\"$ obviously intersect at point $\"Q%280%2C7%29\"$ , the y-intercept for both lines.
\n" ); document.write( "We can find the point $\"P\"$ where $\"green%28y=-0.5x%2B7%29\"$ and $\"blue%28y=2x-3%29\"$ intersect
\n" ); document.write( "by solving $\"system%28green%28y=-0.5x%2B7%29%2Cblue%28y=2x-3%29%29\"$
\n" ); document.write( "I wanted to graph anyway, and in the graph it looked like it was $\"P%284%2C5%29\"$ .
\n" ); document.write( "Substituting $\"x=4\"$ to see that $\"y=5\"$ for both lines confirmed that solution:
\n" ); document.write( " $\"green%28y=-0.5%2A4%2B7=-2%2B7=5%29\"$ and $\"blue%28y=2%2A4-3=8-3=5%29%29\"$ \r
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\n" ); document.write( "The distance from $\"Q%7B0%2C7%29\"$ and $\"P%284%2C5%29\"$
\n" ); document.write( "is the distance between $\"red%28y=2x%2B7%29\"$ and $\"blue%28y=2x-3%29\"$ .
\n" ); document.write( "The distance between two points can be calculated according to a formula:
\n" ); document.write( " $\"PQ=sqrt%28%28x%5BP%5D-x%5BQ%5D%29%5E2%2B%28y%5BP%5D-y%5BQ%5D%29%5E2%29\"$ ,
\n" ); document.write( "but there is no need (usually) to memorize formulas,
\n" ); document.write( "if you understand their meaning.
\n" ); document.write( "That distance is the hypotenuse of a right triangle,
\n" ); document.write( "like the one in my drawing,
\n" ); document.write( "whose legs, parallel to the x-axis and y-axis,
\n" ); document.write( "are the horizontal distance and the vertical distance between the points.
\n" ); document.write( "In this case,
\n" ); document.write( " $\"distance=sqrt%284%5E2%2B2%5E2%29=sqrt%2816%2B4%29=sqrt%2820%29=2sqrt%285%29=about4.47\"$ (rounded). \n" ); document.write( "

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