geometry

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The graphs y=2x+1 and 2y+x=2 contain 2 sides of a rectangle.if 1 vertex of the rectangle has coordinates (6,3), draw the rectangle.

  • geometry -

    y = 2x + 1
    and
    2y + x = 2
    2y = -x + 2
    y =(-1/2)x + 1 , both have the same y-intercept of (0,1)
    So one vertex of the rectangle is (1,0)
    Pick any other point on each of the lines and draw the lines

    since the slopes of the two lines are negative reciprocals of each other you must have a 90° angle at (1.0)
    So all you have to do is create the two lines through (6,3) that have slopes of 2 and -1/2.

    1st line: from (6,3) step 1 to the right, then up 2
    mark that point, draw line through (6,3) and extend
    2nd line: from (6,3) step -2 to the left, then up 1, mark that point, draw the line through 6,3.

    There is your rectangle!

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