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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 20th December 2018, 7:53 PM
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 :
Answered by Expert 21st December 2018, 7:27 AM
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