NCERT Class 11-Math՚S: Exemplar Chapter – 10 Straight Lines Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 10:

A ray of light coming from the point is reflected at a point A on the x-axis and then passes through the point . Find the coordinates of the point A.

Answer:

Let the incident ray strike x-axis at the point A whose coordinates be . From the figure, the slope of the reflected ray is given by

Again, the slope of the incident ray is given by

Or

Solving (1) and (2) , we get

Therefore, the required coordinates of the point A are

Question 11:

If one diagonal of a square is along the line and one of its vertex is at , then find the equation of sides of the square passing through this vertex.

Answer:

Let ABCD be the given square and the coordinates of the vertex D be . We are required to find the equations of its sides DC and AD.

Given that BD is along the line , so its slope is (Why?) The angles made by BD with sides AD and DC is (Why?) . Let the slope of DC be . Then

or

or , which gives

Therefore, the equation of the side DC is given by

Similarly, the equation of another side AD is given by

Objective Type Questions

Each of the Examples 12 to 20 has four possible options out of which only one option is correct. Choose the correct option (M. C. Q.) .

Question 12:

The inclination of the line with the positive direction of x-axis is

(A)

(B)

(C)

(D)

Answer:

(A) is the correct answer. The equation of the line can be rewritten as and hence .

Question 13:

The two lines and are perpendicular if

(A)

(B)

(C)

(D)

Answer:

(A) Is correct answer. Slope of the line is and the slope of the line is The lines are perpendicular if