Question

find the equation to the straight line which bisects and is perpendicular to the straight line joining the points A(a,b) and B(a',b')

Answer 1

Can you find the slope of this line ? which joins the points A(a,b) and B(a',b') ?

Answer 2

and since the given point bisects this line, also find the midpoint

Answer 3

it wil be b'-b /a'-a

Answer 4

i hve the equation of AB as y-b=\[\frac{ b'-b }{ a'-a }(x-a)\]

Answer 5

yes, correct.
and you know what is the product of slopes of perpendicular lines ?

Answer 6

\[i.e. y(a'-a)-x(b'-b)=a'b-ab'\]

Answer 7

equation to line perpendicular to AB is of form \[(b'-b)y+(a'-a)x+k=0\]

Answer 8

correct, so u only need k now, right ?

Answer 9

since the required line bisects AB, if we find the mid-point, that point will lie on the required line, right ? got this ?

Answer 10

yaa how am i going to get its value