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**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

**2. Passing through the point **** with slope **

**Ans. **Given: and

**3. Passing through (0, 0) with slope **

**Ans. **Given: and slope =

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

**Ans. **Given: and

Now,

=

=

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

**Ans. **Given: and

**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

**7. Passing through the points **** and **

**Ans. **Given: and

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

**Ans. **Given: and

**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

**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.

**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

**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

**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

**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

**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

**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)

**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

**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

**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

**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.

thanks

Thanks for help

very nyc sir

thanks sir jii