Question

if x+y=4 is the perpendicular bisector of AB where A=(3 and-3) then B is

Answer 1

Answer: The answer is B(7, 1).

Step-by-step explanation:  As given in the question and shown in the attached figure, the line CD : x + y = 4 is the perpendicular bisector of line AB, where the point is (3, -3). We are find the co-ordinates of the point B.

Let B(a, b) be the required co-ordinates.

Now, equation of the perpendicular bisector CD is

$x+y=4\\\\\Rightarrow y=-x+4.$

S, slope, m = -1.

Therefore, the slope of AB will be

$m^\prime=-\dfrac{1}{m}=-\dfrac{1}{-1}=1.$

Also, AB passes through the point A(3, -3), so its equation will be

$y+3=1(x-3)\\\\\Rightarrow x-y=6.$

Now the point 'D', which is the mid-point of AB will on both AB and CD, so we will get its co-ordinates by finding the point of intersection of both AB and CD.

Now, solving, we get

$2x=10\\\\\Rightarrow x=5,$

and

$y=4-5=-1.$

Hence, the point D is (5,-1).

Now, since 'D' is the mid-point of Ab, so we have

$\dfrac{3+a}{2}=5~~\Rightarrow 3+a=10~~\Rightarrow a=7,\\\\\\\dfrac{-3+b}{2}=-1~~\Rightarrow -3+b=-2~~\Rightarrow b=1.$

Thus, the point B is (7, 1).