Q. 105.0( 4 Votes )

Find the equation

Answer :


Let the equation of line AB be x – 4y + 7 = 0


and point C be (-2, 3)


CD is perpendicular to the line AB, and we need to find:


1) Equation of Perpendicular drawn from point C


2) Coordinates of D


Let the coordinates of point D be (a, b)


Also, point D(a, b) lies on the line AB, i.e. point (a, b) satisfy the equation of line AB


Putting x = a and y = b, in equation, we get


a – 4b + 7 = 0 …(i)


Also, the CD is perpendicular to the line AB


and we know that, if two lines are perpendicular then the product of their slope is equal to -1


Slope of AB × Slope of CD = -1




Slope of CD = - 4


Now, Equation of line CD formed by joining the points C(-2, 3) and D(a, b) and having the slope – 4 is


y2 – y1 = m(x2 – x1)


b – 3 = (-4)[a – (-2)]


b – 3 = -4(a + 2)


b – 3 = -4a – 8


4a + b + 5 = 0 …(ii)


Now, our equations are


a – 4b + 7 = 0 …(i)


and 4a + b + 5 = 0 …(ii)


Multiply the eq. (ii) by 4, we get


16a + 4b + 20 = 0 …(iii)


Adding eq. (i) and (iii), we get


a – 4b + 7 + 16a + 4b + 20 = 0


17a + 27 = 0


17a = -27



Putting the value of a in eq. (i), we get




92 – 68b = 0


-68b = -92





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