Answer

Verified

449.4k+ views

Hint: It is given that the line intersects the x-axis and the y-axis at a certain point. Whenever a line intersects at the x-axis then the point of intersection can be taken as (x, 0) and when it cuts the y-axis the point of intersection is taken as (0, y). Using this concept along with the basic formula of the midpoint of any two points (x, y) and (p, q) we can get the answer.

Complete step-by-step answer:

Consider the line as shown in figure it intersects the y-axis and x-axis at points P and Q respectively.

Therefore the coordinates of P is (x, 0) and the coordinates of Q is (0, y).

And it is given that the midpoint of the line is (2, -5).

As we see that in the above coordinate x is positive and y is negative therefore the line is in the fourth quadrant as in the fourth quadrant x is positive and y is negative.

Now, apply the midpoint property, if (a, b) is the midpoint of the points (e, f) and (g, h).

$ \Rightarrow a = \dfrac{{e + g}}{2},{\text{ }}b = \dfrac{{f + h}}{2}$ So, use this property we have,

As (2, -5) is the midpoint of (x, 0) and (0, y)

$ \Rightarrow 2 = \dfrac{{x + 0}}{2},{\text{ }} - 5 = \dfrac{{0 + y}}{2}$

$ \Rightarrow 4 = x + 0,{\text{ - 10}} = 0 + y$

$ \Rightarrow x = 4{\text{ & }}y = - 10$

Therefore the coordinates of P is (4, 0) and the coordinates of Q is (0, -10)

So, this is the required answer.

Note: Whenever we face such type of problems the key concept is about the understanding that any general point on x axis can be taken as (x, 0) as the y-coordinate on x axis is zero, similarly any general point on y axis can be taken as (0, y) as the x-coordinate on y-axis is zero. Having the basic idea of the midpoint formula can also help getting the right answer.

Complete step-by-step answer:

Consider the line as shown in figure it intersects the y-axis and x-axis at points P and Q respectively.

Therefore the coordinates of P is (x, 0) and the coordinates of Q is (0, y).

And it is given that the midpoint of the line is (2, -5).

As we see that in the above coordinate x is positive and y is negative therefore the line is in the fourth quadrant as in the fourth quadrant x is positive and y is negative.

Now, apply the midpoint property, if (a, b) is the midpoint of the points (e, f) and (g, h).

$ \Rightarrow a = \dfrac{{e + g}}{2},{\text{ }}b = \dfrac{{f + h}}{2}$ So, use this property we have,

As (2, -5) is the midpoint of (x, 0) and (0, y)

$ \Rightarrow 2 = \dfrac{{x + 0}}{2},{\text{ }} - 5 = \dfrac{{0 + y}}{2}$

$ \Rightarrow 4 = x + 0,{\text{ - 10}} = 0 + y$

$ \Rightarrow x = 4{\text{ & }}y = - 10$

Therefore the coordinates of P is (4, 0) and the coordinates of Q is (0, -10)

So, this is the required answer.

Note: Whenever we face such type of problems the key concept is about the understanding that any general point on x axis can be taken as (x, 0) as the y-coordinate on x axis is zero, similarly any general point on y axis can be taken as (0, y) as the x-coordinate on y-axis is zero. Having the basic idea of the midpoint formula can also help getting the right answer.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How many crores make 10 million class 7 maths CBSE

The 3 + 3 times 3 3 + 3 What is the right answer and class 8 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE