MATHEMATICAL PROOFS | PROOF OF P(X,Y) DIVIDES LINESEGMENT AB IN THE RATIO [ X1-X : X-X2 ] | BY VINAY

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MATHEMATICAL PROOFS | THE LINESEGMENT DIVIDES BY X-AXIS AND Y-AXIS IN THE RATIO [-Y1:Y2] & [-X1:X2] MATHEMATICAL PROOFS | THE LINESEGMENT DIVIDES BY X-AXIS AND Y-AXIS IN THE RATIO [-Y1:Y2] & [-X1:X2]
the line segment joining A ( x1, y1) & B( x2, y2 ) in the ratio x1-x:x-x2 or y1-y:y-y2 the line segment joining A ( x1, y1) & B( x2, y2 ) in the ratio x1-x:x-x2 or y1-y:y-y2
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Division of a Line Segment: Midpoint (ratio, r = 1/2): x = (x1+x2)/2, and y = (y1+y2)/2 Division of a Line Segment: Midpoint (ratio, r = 1/2): x = (x1+x2)/2, and y = (y1+y2)/2
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If the point (x, y) is equidistant from the points (a+b,b-a) and (a-b,a+b), prove that bx=ay If the point (x, y) is equidistant from the points (a+b,b-a) and (a-b,a+b), prove that bx=ay