
The diagonals of a square are along the pair of lines whose equation is . If is a vertex of the square, then the vertex of the square adjacent to it maybe
A.
B.
C.
D.
Answer
490.2k+ views
Hint: We will draw the plot of the square on the graph and from reference of the graph, we will substitute in the given equation for the value of y – coordinate corresponding to . Similarly, we will calculate the x – coordinate by putting in the equation. This way we will get all four vertices and then, we will see which of the options verify the answer obtained.
Complete step-by-step answer:
We are given that the diagonals of a square are along the pair of lines whose equation is .
One of the vertices of the square is given as . We are required to find the vertex of the square adjacent to this vertex.
Now, we know that if one vertex is then its adjacent vertices will have their x – coordinates equal to 2 as well. Putting in the equation for the value of y – coordinate (since diagonals are along the pair of lines represented by this equation and hence vertices will also lie on this equation)., we get
Factoring this equation, we will get the values of y as:
Therefore, or . So, the vertices will be .
Again, putting the value of , we get
Factorising this equation for the value of x, we get
Therefore, or . So, the vertices will be .
So, the two vertices adjacent to are .
The graph of the square and pair of the lines can be represented as:
Here, ABCD is the square whose diagonals are along the pair of lines with equation represented by blue coloured lines.
Now, both of these vertices don't match with any of the given options. So, we will simplify these vertices. We can shift the vertices in such a manner that they are adjacent to the vertex multiplying the vertex by 2 and dividing the vertex by 2. We get the vertices and .
Looking at the options, we get that option (C) and option (D) are correct.
Note: In this question, be careful when we have used simultaneously as we need to find the value of the other adjacent vertices. You may go wrong while plotting the graph of the square whose diagonals are along the equation of pair of lines: and hence deducing the vertices adjacent to .
Complete step-by-step answer:
We are given that the diagonals of a square are along the pair of lines whose equation is
One of the vertices of the square is given as
Now, we know that if one vertex is
Factoring this equation, we will get the values of y as:
Therefore,
Again, putting the value of
Factorising this equation for the value of x, we get
Therefore,
So, the two vertices adjacent to
The graph of the square and pair of the lines can be represented as:

Here, ABCD is the square whose diagonals are along the pair of lines with equation
Now, both of these vertices don't match with any of the given options. So, we will simplify these vertices. We can shift the vertices in such a manner that they are adjacent to the vertex
Looking at the options, we get that option (C) and option (D) are correct.
Note: In this question, be careful when we have used
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