Ncert Solutions for class 11 subject Maths Chapter 10 Straight Linesin pdf Best Free NCERT Solutions for class 1 to 12 in pdf NCERT Solutions, cbse board, Maths, ncert Solutions for Class 11 Maths, class 11 Maths ncert solutions, Straight Lines, Class 11, ncert solutions chapter 10 Straight Lines, class 11 Maths, class 11 Maths ncert solutions, Maths ncert solutions class 11, Ncert Solutions Class 11 Mathematics Chapter 10 Straight Lines

Explanation of formula of class 11 mathematics chapter 10 straight line distance formula, section formula , midpoint formula, area of triangle when 3 coordinate points are given

**Question 1:** **Draw a quadrilateral in the Cartesian plane, whose vertices are (β4, 5), (0, 7), (5, β5) and (β4, β2). Also, find its area.**

Answer

Draw a Quadrilateral ABCD whose vertices are A (β4, 5), B (0, 7), C (5, β5), and D (β4, β2).

Area of quadrilateral ABCD = area of βABC + area of βACD

Relate the coordinate of β ABC, A (β4, 5), B (0, 7), C (5, β5) with (x1, y1), (x2, y2), and (x3, y3) and use formula

\[ = \frac{1}{2}|{x_1}({y_2} - {y_3}+{x_2}({y_3} β{y_1} )+ +{x_3}({y_1} β{y_2} |\]

Plug the values, we get

=1/2|-4(7+5) + 0(-5 ,-5) + 5(5-7)|

=1/2|-4(12 +0 + 5(-2)|

=1/2|-48 -10|

=1/2 (58)

=29 unit^{2}

Relate the coordinate of β ABC, A (β4, 5), C (5, β5) and D (β4, β2). with (x1, y1), (x2, y2), and (x3,y3) and use formula

\[ = \frac{1}{2}|{x_1}({y_2} - {y_3}+{x_2}({y_3} β{y_1} )+ +{x_3}({y_1} β{y_2} |\]

Area of βACD

=1/2|-4(-5+ 2) +5(-2-5) + (-4)(5 +5)|

= Β½ |-4(-3) +5(-7) +(-4)(10)|

=1/2|12 -35 -40|

=1/2|-63|

= 63/2 unit^{2 }

Total area of quadrilateral (ABCD) = 29+ 63/2 = 121/2 unit^{2}

**3. Find the distance between P (x1, y1
and Q (x2, y2) when : (i) PQ is parallel to they-axis, (ii) PQ is parallel to the x-axis.
**

**4. Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
**

**5. Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, β 4) and B (8, 0).**

**6. Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and
(β1, β1) are the vertices of a right angled triangle.**

**7. Find the slope of the line, which makes an angle of 30Β° with the positive direction
of y-axis measured anticlockwise.**

**8. Find the value of x for which the points (x, β 1), (2,1) and (4, 5) are collinear.
**

**9. Without using distance formula, show that points (β 2, β 1), (4, 0), (3, 3) and (β3, 2) are the vertices of a parallelogram.
**

**10. Find the angle between the x-axis and the line joining the points (3,β1) and (4,β2).
**

**11. The slope of a line is double of the slope of another line. If tangent of the angle between them is 1/3, find the slopes of the lines.
**

**12. A line passes through (x1, y1) and (h, k). If slope of the line is m, show that k β y1 = m (h β x1).**

**13. If three points (h, 0), (a, b) and (0, k) lie on a line, show that
a/h + b/k = 0**

**14. Consider the following population and year graph (Fig 10.10), find the slope of the line AB and using it, find what will be the population in the year 2010?**

**Question 1-3 (1)Write the equations for the x-and y-axes. (2) Passing through the point (β 4, 3) with slope 1/2
(3) Passing through (0, 0) with slope m.**

**5. Intersecting the x-axis at a distance of 3 units to the left of origin with slope β2.**

**7. Find equation of line passing Passing through the points (β1, 1) and (2, β 4).
**

**8. Find the equation of line whose Perpendicular distance from the origin is 5 units and the angle made by the
perpendicular with the positive x-axis is 30.
**

**9. The vertices of β PQR are P (2, 1), Q (β2, 3) and R (4, 5). Find equation of the median through the vertex R.
**

**10. Find the equation of the line passing through (β3, 5) and perpendicular to the line
through the points (2, 5) and (β3, 6).
**

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

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

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

**14. Find equation of the line through the point (0, 2) making an angle 2Ο/3
with the positive x-axis. Also, find the equation of line parallel to it and crossing the y-axis at a distance of 2 units below the origin.
**

**15. The perpendicular from the origin to a line meets it at the point (β2, 9), find the equation of the line.
**

**16. The length L (in centimetrs) 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.**

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

**18. P (a, b) is the mid-point of a line segment between axes. Show that equation of the line is x/a + y/b = 2**

**19. Point R (h, k) divides a line segment between the axes in the ratio 1: 2. Find equation of the line.
**

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

**1. Reduce the following equations into slope - intercept form and find their slopes
and the y - intercepts.
(i) x + 7y = 0, (ii) 6x + 3y β 5 = 0, (iii) y = 0.
**

**2. Reduce the following equations into intercept form and find their intercepts on the axes.
(i) 3x + 2y β 12 = 0, (ii) 4x β 3y = 6, (iii) 3y + 2 = 0.**

**3. Reduce the following equations into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.
(i) x β3y + 8 = 0, (ii) y β 2 = 0, (iii) x β y = 4.
**

**4. Find the distance of the point (β1, 1) from the line 12(x + 6) = 5(y β 2).**

**5. Find the points on the x-axis, whose distances from the line x/3 + y/4 =1
are 4 units.**

**6. Find the distance between parallel lines(i) 15x + 8y β 34 = 0 and 15x + 8y + 31 = 0 (ii) l (x + y) + p = 0 and l (x + y) β r = 0.
**

**7. Find equation of the line parallel to the line 3x- 4y + 2 = 0 and passing through the point (β2, 3).**

**8. Find equation of the line perpendicular to the line x β 7y + 5 = 0 and having x intercept 3.**

**9. Find angles between the lines
**

**10. The line through the points (h, 3) and (4, 1) intersects the line 7x -9y -19 = 0
at right angle. Find the value of h.
**

**11. Prove that the line through the point (x 1 , y1 ) and parallel to the line Ax + By + C = 0 is A (x βx 1 ) + B (y β y1 ) = 0.**

**12. Two lines passing through the point (2, 3) intersects each other at an angle of 60 If slope of one line is 2, find equation of the other line.
**

**14. Find the coordinates of the foot of perpendicular from the point (β1, 3) to the line 3x β 4y β 16 = 0.**

**15. The perpendicular from the origin to the line y = mx + c meets it at the point (β1, 2). Find the values of m and c.**

**16. If p and q are the lengths of perpendiculars from the origin to the
lines... **

**17. In the triangle ABC with vertices A (2, 3), B (4, β1) and C (1, 2), find the equation
and length of altitude from the vertex A.
**

**18. If p is the length of perpendicular from the origin to the line whose intercepts on ...**

**1. Find the values of k for which the line (kβ3) x β (4 β k2) y + k2 β7k + 6 = 0 is (a) Parallel to the x-axis,
(b) Parallel to the y-axis,
(c) Passing through the origin.
**

**2. Find the values of ΞΈ and p, if the equation x cos ΞΈ + y sinΞΈ = p is the normal form ...**

**3. Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and β 6, respectively.**

**4. What are the points on the y-axis whose distance from the line
is ... 4 units.**

**5. Find perpendicular distance from the origin of the line joining the points (cosΞΈ, sin ΞΈ)
and (cos Ο, sin Ο).**

**6. Find the equation of the line parallel to y-axis and drawn through the point ofintersection of the lines x β 7y + 5 = 0 and 3x + y = 0.**

**7. Find the equation of a line drawn perpendicular to the line ... through the point, where it meets the y-axis.**

**8. Find the area of the triangle formed by the lines y β x = 0, x + y = 0 and x β k = 0.
**

**9. Find the value of p so that the three lines 3x + y β 2 = 0, px + 2 y β 3 = 0 and 2x β y β 3 = 0 may intersect at one point.
**

**10. If three lines whose equations are y = m1x + c1, y = m2x + c2 and y = m
are concurrent, then show that ...**

**11. Find the equation of the lines through the point (3, 2) which make an angle of 45 with the line x β 2y = 3.
**

**12. Find the equation of the line passing through the point of intersection of the lines
4x + 7y β 3 = 0 and 2x β 3y + 1 = 0 that has equal intercepts on the axes**

**13. Show that the equation of the line passing through the origin and making an angle ΞΈ with the line ...**

**14. In what ratio, the line joining (β1, 1) and (5, 7) is divided by the line x + y = 4?
**

**15. Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line 2x β y = 0.
**

**16. Find the direction in which a straight line must be drawn through the point (β1, 2)
so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point.**

**17. The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (β 4, 1). Find the equation of the legs (perpendicular sides) of the triangle.**

**18. Find the image of the point (3, 8) with respect to the line x +3y = 7 assuming the
line to be a plane mirror.**

**23. Prove that the product of the lengths of the perpendiculars drawn from the ...**

**24. A person standing at the junction (crossing) of two straight paths represented by
the equations 2x β 3y + 4 = 0 and 3x + 4y β 5 = 0 wants to reach the path whose
equation is 6x β 7y + 8 = 0 in the least time. Find equation of the path that he
should follow.**

- NCERT Solutions for Class 9 Science Maths Hindi English Math
- NCERT Solutions for Class 10 Maths Science English Hindi SST
- Class 11 Maths Ncert Solutions Biology Chemistry English Physics
- Class 12 Maths Ncert Solutions Chemistry Biology Physics pdf

- Class 1 Model Test Papers Download in pdf
- Class 5 Model Test Papers Download in pdf
- Class 6 Model Test Papers Download in pdf
- Class 7 Model Test Papers Download in pdf
- Class 8 Model Test Papers Download in pdf
- Class 9 Model Test Papers Download in pdf
- Class 10 Model Test Papers Download in pdf
- Class 11 Model Test Papers Download in pdf
- Class 12 Model Test Papers Download in pdf

Copyright @ ncerthelp.com A free educational website for CBSE, ICSE and UP board.