SOLUTION: The co-ordinates of the vertex A of a square ABCD are (1,2) and the equation of the diagonal BD is x+2y=10.Find the equation of the other diagonal and the co-ordinates of centre of

Algebra ->  Coordinate-system -> SOLUTION: The co-ordinates of the vertex A of a square ABCD are (1,2) and the equation of the diagonal BD is x+2y=10.Find the equation of the other diagonal and the co-ordinates of centre of      Log On


   

Question 550393: The co-ordinates of the vertex A of a square ABCD are (1,2) and the equation of the diagonal BD is x+2y=10.Find the equation of the other diagonal and the co-ordinates of centre of the square.pls...help me
Answer by KMST(5328) About Me  (Show Source):
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The diagonals of a square are perpendicular, so you need to find the equation of the line that contains AC, perpendicular to x%2B2y=10, and passing through A (1, 2).
The line that contains BD is described by the equivalent equations
x%2B2y=10 --> 2y=-x%2B10 --> y=%28-1%2F2%29x%2B5.
So the slope of that line is -1%2F2.
The slope of all lines perpendicular to that line is
%28-1%29%2F%28-1%2F2%29=2.
The equation of a line with slope 2 passing through point (1, 2) is
y-2=2%28x-1%29 --> y-2=2x-2 --> y=2x.
So the equations of the two diagonals are
y=2x for the line containing AC, and
x%2B2y=10 for the line containing BD.
They meet at the center of the square. The coordinates of the center of the square can be found by solving the system formed by the to equations.
Substituting y=2x in x%2B2y=10
x%2B2%282x%29=10 -->x%2B4x=10 -->5x=10 -->x=2
Then, y=2x=2%2A2=4
The center of the square is (2,4).