Question

# In the *xy*-plane, the point (2, 6) lies on the graph of where *k *is a constant. Which of the following points must also lie on the graph?

Hint:

**Hint:**

Here, we are given a point on the xy plane and an equation which that point satisfies. This should help us to find the unknown constant k. By using this value of k, we get an equation that is satisfied by the point (2, 6). Next, we check which of the points given in the options satisfy this equation.

## The correct answer is:

### Given, the point (2, 6) satisfies the equation

So, we get

k = 12

Thus, the equation becomes

Next, we check which of the points in the options satisfy the equations

A) (1 , 3)

We can see that , that is

So, (1, 3) doesn’t satisfy the equation

B) (1, 4)

Clearly ,, that is,

So, (1, 4) does not satisfy the equation

C) (3, 3)

Here , , that is ,

Hence, (3, 3) also doesn’t satisfy the equation

D) (3, 4)

Clearly, , so we can say that the point (3, 4) satisfies the equation

The correct option is D) (3, 4).

.

**Note: **

Whenever there is an unknown constant in the given equation, we must always try to find the value of that constant first with the help of the given conditions. Another way to solve this question is; observe that the equation can be written as x y = k , that is, the product of the x co-ordinate and y co-ordinate always remains a constant. As the point (2, 6) satisfies it, we get that constant to be 12. So we check for which of the points in the options, the product of x co-ordinate and y co-ordinate is 12.

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