Question

One vertex of a square ABCD is
A(-1,1) and the equation of one diagonal BD is 3x+y-8=0 then
C=​

Answer 1

Answer:

Let point C(x,y).

Slope of AC=  

x+1

y−1

​

 

and slope of BD=3x+y−8=0

y=−3x+8→(i)

⇒SlopeofBDis−3

⇒AC⊥BD

⇒  

x+1

y−1

​

×−3=−1

⇒3(y−1)=x+1

⇒3y−3=x+1

⇒3y−x=4→(ii)

​

 

Solving equation (i) and (ii)  

⇒  

20

x

​

=  

20

y

​

=  

20

1

​

 

∴x=2,y=2

⇒then,byusingmidformula,  

2

x−1

​

=2,x=5

2

y+1

​

=2,y=3

​

 

Step-by-step explanation: