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Q) Find the distance between A(2,3) on the line of slope 3/4 and the point of intersection P of this line with 5x+7y+40=0.
Asked by Anish | 20 Dec, 2018, 19:53: PM
answered-by-expert Expert Answer
Let the line where the point A lies be,   y = mx+c  ...............(1)
where m is slope and c is y-intercept .
since the line pass through A(2,3) and its slope is 3/4, we get c intercept as :  3 = (3/4)(2) + c  or  c = 3/2
 
hence eqn.(1) is rewritten  as : y =(3/4)x + (3/2)  or 3x-4y = -6
 
To get point of intersection, we solve the following equations.
 
3x - 4y = -6     and     5x +7y = -40
 
we get x = -606/123   and y = -90/41
 
to get distance d : begin mathsize 12px style d space equals space square root of open parentheses 2 plus 606 over 123 close parentheses squared space plus space open parentheses 3 plus 90 over 41 close parentheses squared end root space almost equal to space 8.7 end style
Answered by Thiyagarajan K | 21 Dec, 2018, 07:27: AM

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