NCERT Class 11 Mathematics Solutions: Chapter 10 –Straight Lines Miscellaneous Exercise 10 Part 9

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In figure equation of straight line is shown.

Equation of Straight Line

In figure equation of straight line is shown.

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

Point a and B

The perpendicular bisector of AB.

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 .