Important Questions for CBSE Class 11 Maths Chapter 10 - Straight Lines
CBSE Class 11 Maths Chapter-10 Important Questions - Free PDF Download
1 Marks Questions
1. Find the slope of the lines passing through the point (3,-2) and (-1,4)
Ans. Slope of line through (3,-2) and (-1, 4)
2. Three points 
and 
lie on a line. Show that 
Ans. Since P, Q, R are collinear
Slope of PQ= slope of QR
3. Write the equation of the line through the points 
and 
Ans. Req. eq. 
4. Find the measure of the angle between the lines 
and 
Ans.
Slopes of the two lines are 1 and -1 as product of these two slopes is -1, the lines are at right angles.
5. Find the equation of the line that has y-intercept 4 and is 
to the line 
Ans.
Slope 
=
slope of any line it is 
Req. eq. is 
6. Find the equation of the line, which makes intercepts -3 and 2 on the 
and 
-axis respectively.
Ans. Req. eq. 
2x - 3y + 6 = 0
7. Equation of a line is 
find its slope.
Ans. 
8. Find the distance between the parallel lines
and 
Ans. 
and 
9. Find the equation of a straight line parallel to -axis and passing through the point (4,-2)
Ans. Equation of line parallel to -axis is 
Eq. 
passing through (-4,2)
So 
10. If 
and 
represent the same straight line, find the values of a and b.
Ans. ATQ
11. Find the distance between 
and 
when PQ is parallel to the -axis.
Ans. When PQ is parallel to the -axis,
Then 
12. Find the slope of the line, which makes an angle of 
with the positive direction of -axis measured anticlockwise.
Ans. Let 
be the inclination of the line
13. Determine so that the inclination of the line containing the points 
and 
is 135.
Ans.
14. Find the distance of the point 
from the line 
Ans. Let d be the req. distance
15. Find the value of for which the points 
and 
are collinear.
Ans. Let 
Slope of AB= Slope of BC
16. Find the angle between the -axis and the line joining the points 
and 
Ans. 
[Slope of -axis]
slope of line joining points and
17. Using slopes, find the value of for which the points and are collinear.
Ans. Since the given points are collinear slope of the line joining points 
and 
=slope of the line joining points and
18. Find the value of 
so that the line 
may be parallel to
Ans. ATQ
Slope of 1st line = slope of 2nd line
19. Find the value of , given that the distance of the point from the line 
is 4 units.
Ans. We are given that distance of (4,0) from the line 
is 4
20. Find the equation of the line through the intersection of 
which cuts off equal intercepts on the axes.
Ans. Slope of a line which makes equal intercept on the axes is -1any line through the intersection of given lines is
21. Find the distance of the point 
from the line 
Ans. 
22. Find the equation of a line whose perpendicular distance from the origin is 5 units and angle between the positive direction of the -axis and the perpendicular is 
Ans. 
Req. eq. 
23. Write the equation of the lines for which 
where Q is the inclination of the line andintercept is 4.
Ans. 
and
24. Find the Angle between the -axis and the line joining the points and
Ans. Let 
Slope of 
25. Find the equation of the line intersecting the -axis at a distance of 3 unit to the left of origin with slope -2.
Ans. The line passing through (-3,0) and has slope = -2
Req. eq. is
4 Marks Questions
1. If p is the length of the 
from the origin on the line whose intercepts on the axes are a and b. show that 
Ans. Equation of the line is 
The distance of this line from the origin is P
Sq. both side
2.Find the value of p so that the three lines 
and 
may intersect at one point.
Ans. 
On solving eq. 
and 
And 
Put 
in eq. 
3.Find the equation to the straight line which passes through the point (3,4) and has intercept on the axes equal in magnitude but opposite in sign.
Ans. Let intercept be a and –a the equation of the line is
Since it passes through the point (3, 4)
Put the value of a in eq. (i)
4.By using area of 
. Show that the points 
and 
are collinear.
Ans. Area of 
5. Find the slope of a line, which passes through the origin, and the midpoint of the line segment joining the point 
and 
Ans. Let 
be the midpoint of segment PQ then 
Slope of 
6.Find equation of the line passing through the point 
and cutting off intercepts on the axes whose sum is 9
Ans. Req. eq. be 
This line passes through
7.Reduce the equation 
into normal form. Find the values p and
.
Ans.
Dividing by 2
Comparing with
8. Without using the Pythagoras theorem show that the points 
and 
are the vertices of a right angled .
Ans. The given points are 
and 
Slope of 
Slope of 
Slope of 
Slope of 
slope of 
Hence ABC is right angled at A.
9.The owner of a milk store finds that, he can sell 980 liters of milk each week at 14 liter and 1220 liter of milk each week at Rs 16 liter. Assuming a linear relationship between selling price and demand how many liters could he sell weekly at Rs 17 liter?
Ans. Assuming sell along 
-axis and cost per litre along 
-axis, we have two points 
and 
in plane
When 
litres.
10.The line through the points (h,3) and (4,1) intersects the line 
at right angle. Find the value of h.
Ans. Slope of line joining (h,3) and (4,1)
Given line is
Slope of this line = 
ATQ
11.Find the equations of the lines, which cut off intercepts on the axes whose sum and product are 1 and -6 respectively.
Ans. ATQ 
Put b in eq.
When 
Eq. of the line is
When 
Eq. of the line is
12. The slope of a line is double of the slope of another line. If tangent of the angle between them is 
, find the slopes of the lines.
Ans. Let the slope of one line is and other line is 
13.Point 
divides a line segment between the axes in the ratio 1:2. Find equation of the line.
Ans. Let eq. be 
It is given that divides AB in the ratio 1:2
Put a and b in eq.………
14.The Fahrenheit temperature F and absolute temperature K satisfy a linear equation. Given that K=273 when F=32 and that K= 373 when F=212 Express K in terms of F and find the value of F when K=0
Ans. Let F along -axis and K along -axis
15. If three points 
and 
lie on a line, show that 
Ans. Let 
Slope of AB = slope of BC
16.
is the mid point of a line segment between axes. Show that equation of the line is 
Ans. Req. eq. be
P is the mid point
Coordinate of 
Put the value of C and D in eq. (i)
17.The line to the line segment joining the points 
and 
divides it in the ratio 
find the equation of the line.
Ans. Coordinate of 
Eq. of PQ is
6 Marks Questions
1. Find the values of 
for the line 
(a). Parallel to the 
-axis
(b). Parallel to 
-axis
(c). Passing through the origin
Ans.
(a) The line parallel to -axis if coeff. Of =0
(b) The line parallel to -axis if coeff. Of =0
(c)Given line passes through the origin if (0, 0) lies on given eq.
2. If p and q are the lengths of 
from the origin to the lines.
and 
respectively, prove that 
Ans.
Squaring 
and
and adding
3.Prove that the product of the drawn from the points 
and 
to the line 
is 
.
Ans. Let
Similarly 
be the distance from to given line
4. Find equation of the line mid way between the parallel lines 
and 
Ans. The equations are
Let the eq. of the line mid way between the parallel lines (i) and (ii) be
ATQ
Distance between (i) and (iii) = distance between (ii) and (iii)
Req. eq. is
5. Assuming that straight lines work as the plane mirror for a point, find the image of the point (1,2) in the line 
Ans.Let 
is the image of the point 
in the line.
Coordinate of midpoint of 
This point will satisfy the eq. ……(i)
(Slope of line PQ) 
slope of line 
On solving (i) and (ii)
and 
6.A person standing at the junction (crossing) of two straight paths represented by the equations 
and 
wants to reach the path whose equation is 
in the least time. Find equation of the path that he should follow.
Ans. 
On solving eq. (i) and (ii)
We get 
To reach the line (iii) in least time the man must move along the from crossing point to (iii) line
Slope of (iii) line is 
Slope of required path 
7. A line is such that its segment between the lines 
and 
is bisected at the point 
obtain its equation.
Ans. 
lies on 
And 
lies on 
On solving
Since R is the mid point of PQ
On solving
And 
Eq. of PQ
8.Find the equations of the lines which pass through the point 
and make equal angles with the lines 
and 
Ans. The slopes of the given lines are 
and 
Let m be the slope of a required line
ATQ
Neglect
Req. eq. are
