# NCERT Class 11-Math՚s: Exemplar Chapter – 10 Straight Lines Part 4 (For CBSE, ICSE, IAS, NET, NRA 2023)

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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