CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Combination Based on Geometry

In a plane, t...

Question

In a plane, there are two families of lines $y = x + k, y = - x + k,$ where $k \in {0, 1, 2, 3, 4}$ . The number of squares with diagonal of length $2$ units formed by the lines, is

Open in App

Solution

Consider the lines $L_{1}, L_{3}$ .
The lines $L_{1}, L_{3}$ form square with diagonal of length $2$ unit with lines $M_{1}, M_{3}$ and $M_{2}, M_{4}$ and $M_{3}, M_{5}$
So, for $L_{1}, L_{3}$ , the number of such squares is $3$

As there are $3$ choices $((L_{1}, L_{3}), (L_{2}, L_{4}) (L_{3}, L_{5}))$ for the family $y = x + k$ ,
the total number of such squares is $3 \times 3 = 9$

Suggest Corrections

thumbs-up

1

Similar questions

Q. In a plane, there are two families of lines

y = x + k, y = - x + k,

k \in {0, 1, 2, 3, 4}

. The number of squares with diagonal of length

2

units formed by the lines, is

Q. In a plane there are two families of lines y

=

=

r \in 0, 1, 2, 3, 4

. The number of squares of diagonals of the length 2 units formed by the lines is

Q. In a plane there are two families of lines

y = x + r, y = - x + r

r \in {0, 1, 2, 3, 4}

.The number of squares that can be formed from these family of lines such that its diagonal is of length

2

Q. In a plane there are two families of lines

y = x + r, y = - x + r

r \in {0, 1, 2, 3, 4}

.The number of squares that can be formed from these family of lines such that its diagonal is of length

2

Q. Consider the fourteen lines in a plane given by y = x + r, y = -x + r where r= 0,1,2,3,4,5,6 The number of squares formed by these lines whose diagonals are of length 2 is

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Combination Based on Geometry

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon