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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
answered-by-expert 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
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
determine graphically the vertices of the traingle 3x+3y=10
Asked by bhunias174 | 30 Mar, 2022, 09:45: PM
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CBSE 11-science - Maths
find a and b so that the lines ax+8y+b=0,2x+ay-1=0 may be parallel or perpendicular  
Asked by ankitakhokhar56 | 06 Dec, 2019, 02:51: PM
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CBSE 11-science - Maths
If space p space i s space t h e space l e n g t h space o f space p e r p e n d i c u l a r space d r a w n space f r o m space o r i g i n space t o space l i n e space x over a plus y over b space equals space 1 space a n d space a squared comma p squared comma b squared space a r e space i n space A. P. space comma space t h e n space p r o v e space t h a t space a to the power of 4 plus b to the power of 4 space equals space 0 space.
Asked by manish.kkd4 | 20 Feb, 2019, 12:20: PM
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CBSE 11-science - Maths
Find the coordinates of point C, which divides the line segment joining the points D (-2, 5) and E (4, 6) in the ratio 2 : 3.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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CBSE 11-science - Maths
If the slope of line joining the points (2, 3) and (4, -5) is equal to the slope of line joining the points (x, 5) and (5, 6). Find the value of x.
Asked by Topperlearning User | 26 Sep, 2014, 09:43: AM
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CBSE 11-science - Maths
Find the slope of line which passes through the point (5, 6) and the mid-point of line joining the points (4, 6) and (-3, 7).
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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CBSE 11-science - Maths
Find the point which divides the line segment joining the points A (5, 7) and B (8, 4) in the ratio 3 : 5.
Asked by Topperlearning User | 26 Sep, 2014, 01:57: PM
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CBSE 11-science - Maths
If three points (3, 6), (-5, 7) and (x, 1) are collinear, find the value of x.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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CBSE 11-science - Maths
Find a point on the Y-axis, which is equidistant from the points (-3, 4) and (5, 6).
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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