ncert cbse chapter 10 straight lines exercise 10.2
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?
choose x as selling price per litre in rupees and y as demand in litres
the line passes through (14,980 ) and (16,1220)
using 2 point form equation of the line is
[(y-980)/(1220-980)] = [(x-14)/(16-14)]
(y-980)/240 = (x-14)/2
y-980 = 120(x-14)
y-980 = 120x -1680
y = 120x-1680+980
y = 120x -700
now put x = 17
y = 120*17 -700
y = 1340 litres
13. Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
let the intercepts be a and b
given a+b = 9
b = (9-a)
using intercept form of straight line
required equation is
[x/a] + [y/b] =1
change b = (9-a) to get
[x/a] + [y/ (9-a)] =1--------------(1)
this passes through (2,2)
so
[2/a] + [2/ (9-a)] =1
[ 2(9-a) +2a ] / [a(9-a)] = 1
[18 ]/ [a(9-a)] = 1
18 = [a(9-a)]
18 = 9a -(a^2)
(a^2) - 9a +18 = 0
(a-3)(a-6) =0
a = 3 or a=6
use in eqn(1) to get
2x+y =6 or x+2y =6
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ncert cbse chapter 10 straight lines miscellaneous exercise
24. A person standing at the junction (crossing) of two straight paths represented by the equations 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 wants to reach the path whose equation is 6x – 7y + 8 = 0 in the least time. Find equation of the path that he should follow.
22. A ray of light passing through the point (1, 2) reflects on the
x-axis at point A and the reflected ray passes through the point (5, 3).
Find the coordinates of A.
21. Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 =0
19. If the lines y = 3x +1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find the value of m.
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.
17. The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (– 4, 1). Find an equation of the legs (perpendicular sides) of the triangle
14. In what ratio, the line joining (–1, 1) and (5, 7) is divided by the
line x + y = 4 ?
12.Find the equation of the line passing through the point of
intersection of the lines 4x + 7y – 3 = 0 and 2x – 3y + 1 = 0 that has
equal intercepts on the axes
11. Find the equation of the lines through the point (3, 2) which make an angle of 45 degrees with the line x – 2y = 3.
8. Find the area of the triangle formed by the lines y – x = 0, x + y = 0
and x – k = 0
solution9. Find the value of p so that the three lines 3x + y – 2 = 0, px + 2 y – 3 = 0 and
2x – y – 3 = 0 may intersect at one point.
6. Find the equation of the line parallel to y-axis and drawn through the point of
intersection of the lines x – 7y + 5 = 0 and 3x + y = 0.
4. What are the points on the y-axis whose distance from the line
[x/3] + [y/4]=1 is 4 units.
3. Find the equations of the lines, which cut-off intercepts on the axes whose sum
and product are 1 and – 6, respectively.
2. Find the values of θ and p, if the equation x cos θ + y sin θ = p is the normal form of the line [sqrt(3)] x + y + 2 = 0.
Find the values of k for which the line
(k–3) x – (4 –( k^ 2) ) y + (k^2) –7k + 6 = 0 is
(a) Parallel to the x-axis,
(b) Parallel to the y-axis,
(c) Passing through the origin.
ncert cbse chapter 10 exercise 10.3
17. In the triangle ABC with vertices A (2, 3), B (4, –1) and C (1, 2), find the equation and length of altitude from the vertex A.
14. Find the coordinates of the foot of perpendicular from the point (–1, 3) to the
line 3x – 4y – 16 = 0.
13. Find the equation of the right bisector of the line segment joining the points
(3, 4) and (–1, 2).
10. The line through the points (h, 3) and (4, 1) intersects the line
7 x − 9 y − 19 = 0 at right angle. Find the value of h.
8. Find equation of the line perpendicular to the line x – 7y + 5 = 0 and having
x intercept 3.
exercise 10.2
19. Point R (h, k) divides a line segment between the axes in the ratio 1: 2. Find
equation of the line.
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?
13. Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.
12.Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).
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.
10. Find the equation of the line passing through (–3, 5) and perpendicular to the line through the points (2, 5) and (–3, 6).
9. The vertices of ∆ PQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the
median through the vertex R.
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