Question

equation of diagonal of square formed by line x=0 , y=0, x=1 and y=1 are:

please solve it

Answer 1

A)

 

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Toolbox:Equation of line whose join of points is (x1,y1)(x1,y1) and (x2,y2)(x2,y2)is y−y1y2−y1y−y1y2−y1=x−x1x2−x1=x−x1x2−x1

Step 1 :

The equation of the square formed by the lines are x=0,y=0,x=1andy=1x=0,y=0,x=1andy=1respectively.



Hence the vertices of the square are 0(0,0),A(1,0),B(1,1),C(0,1)0(0,0),A(1,0),B(1,1),C(0,1)respectively

Hence the equation of the diagonals 0B is

y−y1y2−y1y−y1y2−y1=x−x1x2−x1=x−x1x2−x1

(i.e) y−01−0y−01−0=x−01−0=x−01−0

⇒y=x⇒y=x--------(1)

equation of the diagonal AC is

y−01−0y−01−0=x−10−1=x−10−1

⇒−y=x−1⇒−y=x−1

⇒x+y=1⇒x+y=1

Hence 'A' is the correct answer.

Answer 2

coordinates of vertices of square ABCD is (0,0) ,(0,1) , (1,1) (1,0) respectively equation of diagonal AC by applying 2 point form of equation get $y=x$ , that of BD is $y=-x+1$