In what ratio is the line segment joining the points (-4, 2) and (8, 3) divided by -> 2x - 3 = 0

Asked by Simran K | 23rd Feb, 2014, 01:25: PM

Expert Answer:

Let the line segment joining the points (-4,2) and (8,3) divides the line 2x - 3 = 0 in the ratio k:1.
 
Thus, the coordinates of the point of intersection is P open parentheses fraction numerator k x subscript 2 plus x subscript 1 over denominator k plus 1 end fraction comma fraction numerator k y subscript 2 plus y subscript 1 over denominator k plus 1 end fraction close parentheses equals P open parentheses fraction numerator 8 k minus 4 over denominator k plus 1 end fraction comma fraction numerator 3 k plus 2 over denominator k plus 1 end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals P open parentheses fraction numerator 8 k minus 4 over denominator k plus 1 end fraction comma fraction numerator 3 k plus 2 over denominator k plus 1 end fraction close parentheses S i n c e space i t space m e e t s space t h e space l i n e space 2 x minus 3 equals 0 comma space w e space h a v e comma 2 open parentheses fraction numerator 8 k minus 4 over denominator k plus 1 end fraction close parentheses minus 3 equals 0 rightwards double arrow 2 open parentheses 8 k minus 4 close parentheses minus 3 open parentheses k plus 1 close parentheses equals 0 rightwards double arrow 16 k minus 8 minus 3 k minus 3 equals 0 rightwards double arrow 13 k minus 11 equals 0 rightwards double arrow 13 k equals 11 rightwards double arrow k equals 11 over 13
Thus, the line segment divides the line in the ratio 11:13

Answered by  | 25th Feb, 2014, 11:26: AM

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