Home
Class 12
MATHS
Two sides of a square lie on the lines x...

Two sides of a square lie on the lines `x+y=1a n dx+y+2=0.` What is its area?

Text Solution

Verified by Experts

Clearly, the length of the side of the square is equal to the distance between the parallel lines.
`x+y-1=0 " " (1)`
`" and " x+y+2=0 " " (2)`
Hence, side length `=(|2-(-1)|)/(sqrt((1+1))) = (3)/(sqrt(2))`
Therefore, area of square `=(9)/(2)` sq. units.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXAMPLE|12 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.1|23 Videos

  • STRAIGHT LINE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

Similar Questions

Explore conceptually related problems

Two sides of a rhombus are along the lines, x-y+1=0 and 7x-y-5=0 . If its diagonals intersect at (-1,-2) , then which one of the following is a vertex of this rhombus ? (1) (-3,-9) (2) (-3,-8) (3) (1/3,-8/3) (4) (-(10)/3,-7/3)

Two sides of a square are along the straight lines 5x-2y=13 and 5x-2y+16=0 , state which of the following is the length of a side of the square ?

Two sides of a parallelogram are along the lines x+y=3 and x=y+3. If its diagonals intersect at (2, 4) , then one of its vertices is

The sides of a triangle ABC lie on the lines 3x + 4y = 0, 4x +3y =0 and x =3 . Let (h, k) be the centre of the circle inscribed in triangleABC . The value of (h+ k) equals

Two sides of a rhombus are along the lines x - y + 1 = 0 and 7 x - y - 5 = 0 . If its diagonals intersect at ( - 1, -2) , then which one of the following is a vertex of this rhombus ?

Two sides of a square have the equations 5x+12y-10=0 and 5x+12y+29=0. The coordinates of a point on the third side are (3,5) . Find the equations to the other sides of the square.

If two sides of a square are the part of the straight lines 5x-2y=13and5x-2y+16=0 then find the area of the square.

One side of a rectangle lies along the line 4x+7y+5=0. Two of its vertices are (-3,1)a n d(1,1)dot Find the equations of the other three sides.

One diagonal of a square is along the line 8x-15 y=0 and one of its vertex is (1, 2). Then the equations of the sides of the square passing through this vertex are (a)23 x+7y=9,7x+23 y=53 (b)23 x-7y+9=0,7x+23 y+53=0 (c)23 x-7y-9=0,7x+23 y-53=0 (d)none of these

One side of an equilateral triangle is the line 3x+4y+8=0 and its centroid is at P(1,1) . Find the length of a side.