Home
Class 12
MATHS
If one side of the square is 2x-y+6=0, t...

If one side of the square is `2x-y+6=0,` then one of the vertices is `(2,1)` . Find the other sides of the square.

Text Solution

Verified by Experts


Vertex A(2,1) does not lie on the line BC=2x-y+6=0 (1)
Hence, one of the side of the square passing through A is parallel to BC.
Therefore, the equation of AD is
y-1=2(x-2)
`or 2x-y-3=0 " " (2)`
Another side AB of the square is passing through (2,1) and is perpendicular to BC.
Therefore, the equation of AB is
`y-1 = -(1)/(2) (x-2)`
` or x+2y-4=0 " " (3)`
The third side is parallel to AB, which has equation
`x+2y+c=0 " " (4)`
Now, the distance between the lines BC and AD is `9//sqrt(5)`.
Therefore, the distance between the lines (3) and (4) is
`(|C+4|)/(sqrt(5)) = (9)/(sqrt(5))`
`therefore c=5 or -13` Therefore, the equation of the third side is
x+2y+5=0 `(-=C'D')`
`"or " x+2y-13=0 (-=CD)`
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

If one of the sides of a square is 3x-4y-12=0 and the center is (0,0) , then find the equations of the diagonals of the square.

Sum of the areas of two squares is 468 m^(2) . If the difference of their perimeters is 24 m, find the sides of the two squares.

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

The center of a square is at the origin and its one vertex is A(2,1)dot Find the coordinates of the other vertices 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.

CHOOSE the correct answer from the following alternative : the rate of incrse of a side of a square is 1cm/sec. the rate of increase of area of the square, when length os a side of the square is 2 cm , is -

If the area of the square drawn on any side of a triangle is equal to the sum of the areas of the squares drawn on the other two sides of the triangle ,then the triangle will be right-angled triangle, the opposite angle of the greatest side of which will be "......................" .

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.

The equation of a side of a rectangle is 4x+7y+5=0 and the two vertices are (-3,1)&(1,1).Find the equation of other three sides.

One diagonal of a square is 3x-4y+8=0 and one vertex is (-1,1), then the area of square is