NCERT Solutions class-11 Maths Exercise 10.2

Exercise 10.2

In Exercises 1 to 8, find the equations of the line which satisfy the given conditions:

1. Write the equations for the and axis.

Ans. Equation for axis is

Equation for axis is

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2. Passing through the point with slope

Ans. Given: and

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3. Passing through (0, 0) with slope

Ans. Given: and slope =

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4. Passing through and inclined with the axis at an angle of

Ans. Given: and

Now,

=

=

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5. Intersecting the axis at a distance of 3 units to the left of origin with slope

Ans. Given: and

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6. Intersecting the axis at a distance of 2 units above the origin and making an angle of with positive direction of the axis.

Ans. Given: and

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7. Passing through the points and

Ans. Given: and

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8. Perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive axis is

Ans. Given: and

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9. The vertices of PQR are P (2, 1), Q and R (4, 5). Find equation of the median through the vertex R.

Ans. Given: P (2, 1), Q and R (4, 5) are the vertices of . RS is the median through vertex R. Then S is the mid-point of PQ.

Coordinates of S are (0, 2)

Equation of required median RS is

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10. Find the equation of the line passing through and perpendicular to the line through the points (2, 5) and

Ans. Let A (2, 5) and B be any two points.

Slope of AB =

Since, the required line is perpendicular to AB, therefore slope of required line

Also, the required line passing through point having slope 5.

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11. A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio Find the equation of the line.

Ans. Let point C divides the join of A (1, 0) and B (2, 3) in the ratio

Coordinates of C are

And Slope of AB =

Since, the required line is perpendicular to AB, therefore slope of required line

Also, the required line passing through point having slope

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12. Find the equation of the line cuts off equal intercepts on the coordinate axis and passes through the point (2, 3).

Ans. Let equal intercepts on the coordinate axis be and the line passes through point (2, 3).

Therefore, the equation of required line is

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13. Find the equation of the line passing through the point (2, 2) and cutting off intercept on the axis whose sum is 9.

Ans. Given: Line passes through point (2, 2). And

and

and

Therefore, equation of lines are

and

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14. Find equation of the line through the point (0, 2) making an angle with the positive axis. Also find the equation of the line parallel to it and crossing the axis at a distance of 2 units below the origin.

Ans. Given:

Equation of the line passing through point (0, 2) having slope is

Now the line parallel to this line having slope and

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15. The perpendicular from the origin to a line meets it at the point find the equation of the line.

Ans. Here, Slope of the line OP =

Since the required line is perpendicular to OP.

Slope of required line =

Equation of the required line is

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16. The length L (in centimeter) of a copper rod is a linear function of its Celsius temperature C. In an experiment if L = 124.942 when C = 20 and L = 125.134 when C = 110, express L in terms of C.

Ans. Let the length be represented by and the temperature by

= (20, 124.943) and = (110, 125.134)

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17. The owner of a milk store finds that he can sell 980 liters of milk each week at Rs. 14 litre and 1220 liters of milk each week at Rs. 16 liters. Assuming a linear relationship between selling price and demand, how many liters could he sell weekly at Rs. 17 liter?

Ans. Here, = (980, 14) and = (1220, 16)

Putting we have

liters

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18. P is the mid-point of a line segment between axis. Show that equation of the line is

Ans. Let A and B be two points where the line intersect and axis respectively and P is mid-point of AB.

Then

And

Equation of the required line is

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19. Point R divides a line segment between the axis in the ratio 1: 2. Find equation of the line.

Ans. Let A and B be two points where the line intersect and axis respectively and R is a point divides AB in the ratio 1: 2.

and

and

Equation of the required line is

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20. By using concept of equation of a line, prove that the three points (3, 0), and (8, 2) are collinear.

Ans. Here, = (3, 0) and =

Putting the coordinates of third point, we have

16 – 10 = 6

6 = 6

Therefore, third point lies on the line of first two points and given three points are collinear.