NCERT Class 11-Math's: Exemplar Chapter –10 Straight Lines Part 6

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Question 19:

The reflection of the point about the line is

(A)

(B)

(C)

(D)

Answer:

The correct choice is (A). Let be the point of reflection of the given point about the line . The mid-point of the line segment joining points and is given by

This point lies on the given line, so we have

Or

Again the slope of the line joining points and is given by . This line is perpendicular to the given line and hence

This gives

or

On solving (1) and (2), we get and . Thus the point is the reflection of the given point.

Question 20:

A point moves such that its distance from the point is half that of its distance from the line . The locus of the point is

(A)

(B)

(C)

(D) None of these

Answer:

The correct choice is (A). Let (h, k) be the coordinates of the moving point. Then, we have

or

Hence, the required locus is given by

10.3 EXERCISE

Short Answer Type Questions

Question 1:

Find the equation of the straight line which passes through the point and cuts off equal intercepts from axes.

Answer:

Question 2:

Find the equation of the line passing through the point and perpendicular to the line joining the points and .

Answer:

Question 3:

Find the angle between the lines and .

Answer:

Question 4:

Find the equation of the lines which passes through the point and cuts off intercepts from the coordinate axes such that their sum is .

Answer:

Question 5:

Find the points on the line which lie at a unit distance from the line .

Answer:

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