Q10 of 319 Page 23

Find the equation of the straight line which divides the join of the points (2, 3) and ( – 5, 8) in the ratio 3 : 4 and is also perpendicular to it.

Given, A line which divides the join of the points (2,3) and ( – 5,8) in the ratio 3:4

To Find : The equation of the line.


Explanation: The coordinates of the point which divides the join of the points (2,3) and ( – 5,8) in the ratio 3:4 is given by (x,y).


Coordinate of x when line divides in ratio m:n


x =


x =


Coordinate of y when line divides in ratio m:n =


y =


y =


The slope of the line with two points is, m =


Now, The slope of joining the points (2,3) and ( – 5,8) =


m =


The equation of the line is


y


y





35y – 180 = 49x + 63


49x – 35y + 229 = 0


Hence, The equation of line is 49x – 35y + 229 = 0


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