# NCERT Class 11 Mathematics Solutions: Chapter 10 – Straight Lines Miscellaneous Exercise 10 Part 9 (For CBSE, ICSE, IAS, NET, NRA 2022)

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1. Find the direction in which a straight line must be drawn through the point so that its point of intersection with the line may be at a distance of units from this point.

Answer:

Consider be the line through point

Accordingly, .

… eq (1)

The given line is

… eq (2)

On solving equations (1) and (2) , we obtain

and

is the point of intersection of lines eq (1) and (2) .

Since this point is at a distance of units from point , according to distance formula,

So, the slope of the required line must be zero i.e.. , the line must be parallel to the axis.

2. Find the image of the point with respect to the line assuming the line to be a plane mirror.

Answer:

The equation of the given line is … eq (1)

Consider point be the image of point .

Accordingly, line eq (1) is the perpendicular bisector of

Slope of is while the slope of line

Line (1) is perpendicular to ,

… eq (2)

Mid-point of

The mid-point of line segment will also satisfy line (1) .

From equation (1) ,

… eq (3)

On solving equations (2) and (3) , we obtain .

The image of the given point with respect to the given line is .