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CBSE Class 11-science Answered

Three points P(h,k), Q (x,y) and R (x,y) lie on a line show that (h-x) (y-y)= (k-y) (x-x),
Asked by hrai7387 | 16 Jan, 2023, 07:36: PM
Expert Answer
Let (h.k) , (x1 , y1) and (x2 , y2 ) are three given points
 
slope of segment PQ = begin mathsize 14px style fraction numerator left parenthesis y subscript 1 minus k right parenthesis over denominator left parenthesis x subscript 1 minus h right parenthesis end fraction end style
 
slope of segment QR = begin mathsize 14px style fraction numerator left parenthesis y subscript 2 minus y subscript 1 right parenthesis over denominator left parenthesis x subscript 2 minus x subscript 1 right parenthesis end fraction end style
If P, Q and R on same line , then both the above slopes are equal and we have
 
begin mathsize 14px style fraction numerator left parenthesis y subscript 1 minus k right parenthesis over denominator left parenthesis x subscript 1 minus h right parenthesis end fraction end style = begin mathsize 14px style fraction numerator left parenthesis y subscript 2 minus y subscript 1 right parenthesis over denominator left parenthesis x subscript 2 minus x subscript 1 right parenthesis end fraction end style
By cross multiplication of above expression, we get
 
begin mathsize 14px style left parenthesis y subscript 1 space minus space k space right parenthesis space left parenthesis space x subscript 2 minus x subscript 1 right parenthesis space equals space left parenthesis x subscript 1 minus h right parenthesis left parenthesis y subscript 2 minus y subscript 1 right parenthesis end style
Answered by Thiyagarajan K | 16 Jan, 2023, 08:39: PM

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CBSE 11-science - Maths
Three points P(h,k), Q (x,y) and R (x,y) lie on a line show that (h-x) (y-y)= (k-y) (x-x),
Asked by hrai7387 | 16 Jan, 2023, 07:36: PM
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