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CBSE Class 11-science Answered

A Straight line through the origin O meets the parallel lines 4x+ 2y =9 and 2x+ y  +6 =0 at points
 
P and Q respectively. Find the ratio in which the point O divides the line segment PQ.
Asked by ahuja8087 | 14 Mar, 2016, 03:09: PM
answered-by-expert Expert Answer
 
 
begin mathsize 12px style straight Y minus intercept space of space 4 straight x plus 2 straight y equals 9 space is space 9 over 2. Hence comma space OM equals 9 over 2 straight Y minus intercept space of space 2 straight x plus straight y plus 6 equals 0 space is space minus 6. Hence comma space ON equals 6 The space line space passing space through space origin space cuts space the space lines space at space straight P space and space straight Q space respectively. In space triangles space OPM space and space OQM angle POM equals angle QOM angle PMO equals angle QNO Hence comma space both space triangles space are space similar. rightwards double arrow OM over ON equals OP over OQ equals fraction numerator begin display style 9 over 2 end style over denominator 6 end fraction equals 3 over 4 Hence comma space straight O space divides space PQ space in space the space ratio space 3 colon 4. This space is space true space for space any space line space passing space through space the space origin space as We space always space get space similar space triangle space as space above. end style
Answered by satyajit samal | 14 Mar, 2016, 05:03: PM

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