CBSE Class 11 Mathematics Straight Lines Worksheet Set D

Q1. Prove that lines 3x + y – 14 = 0, x – 2y = 0 & 3x – 8y + y = 0 are concurrent. Also find co-ordinates of pt of concurrence.

Q2. Find eq of line which passes through pt. (3, 2) if the portion of line intercepted between the axes is bisected at the point.

Q3. Find the equation of two straight line passing through (4, -2) and making an angle of 450 with the line 8x + 7y -1 = 0. Show that those two lines are at right angles to one another.

Q4. The mid points of the sides of a triangle are (2, 1), (-5, 7) and (-5, -5). Find the equations of the sides.

Q5. Prove that the perpendicular drawn from the point (4, 1) on the join of (2, -1) and (6, 5) divides it in the ratio 5:13.

Q6. Find eq of straight line which passes through pt (22, -6) & is such that intercept on x-axis exceeds intercept on y axis by 5.

Q7. Find the angle between the lines which have intercept 3, 4 and 1, 8 on the axis respectively.

Q8. Find eq of the straight line which cuts off intercept on x axis twice that on y-axis and is at a unit distance from origin.

Q9. Find the equation of a line parallel to 2x + 3y + 11 = 0 and the sum of its intercepts on the axis is 15.

Q10. Find the image of the point (-8, 12) with respect to the line mirror 4x + 7y + 13 = 0

Q11. Find the equation of a line which divides the join of (1, 0) and (3, 0) in the ratio 2:1 and perpendicular to it.

Q12. A line through the points (a, 2a) and (-2, 3) is perpendicular to the line 4x + 3y + 5 = 0, find the value of ‘a’.

Q13. If lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent, show that a, b, c are in A.P.

Q14. Prove that the points (1, 3), (3, 5) and (5, 7) are collinear. Also find the equation of the line.

Q15. Transform the equation of the line x + y + 4 = 0 to (i) slope intercept form and find its slope and y intercept
(ii) intercept from and find intercepts on the coordinate axes (iii) normal form and find the inclination of the perpendicular segment from the origin on the line with x=axis and also find its length.

Q16. Find equation of line passing through interaction of lines x + y + 3 = 0 & x – y + 2 = 0 and having y – intercept equal to 4.

Q17. One side of a rectangle is along line 4x + 7y + 5 = 0. Two of its vertices are (-3, 1) & (1, 1). Find eqs of other three sides.

Q18. The vertices of a triangle are A (-2, 1), B(6, -2) and C (4, 3). Find the lengths of the altitudes of the triangle.

Q19. Find the equations of the lines which are at a distance of ½ from the origin and pass through the point (0,1).

Q20. Find the equation of the line joining the points (3, -1) and (2, 3). Also find equation of line perpendicular to this line and passing through point (5, 2).

Q21 Find the new co-ordinates of the point in each of the following cases if the origin is shifted to the point (-1, -2 ) by translation of axes. 
a) (2,3)
b) ( -5, -4)
c) ( -1, 4)

Q22 Find what the following equation becomes when the origin is shifted to ( 2,3)
a) x² = 4ay
b) x² – y² =4
c) x + 2y =7

Q.1 The length L (in centimetre) 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.

Q.2 Write the equation of a line parallel to x-axis and passing through (-2,3).

Q.3 Point R (h, k) divides a line segment between the axes in the ratio 1:2. Find equation of the line.

Q.4 Find the equation of the straight lien which makes an angle of 60° with the x - axis and cuts of an intercept -2 from the y - axis.

Q.5 Find the equation of the straight line joining the points (a,b) and {(a+b),(a-b)}.

Q.6 Find the slope of a line which passes through (1,2) and (-3,4)?

Q.7 Find the coordinates of point C, which divides the line segment joining the points D (-2, 5) and E (4, 6) in the ratio 2 : 3.

Q.8 If three lines whose equations are y = m₁ x + c₁, y = m₂x + c₂, y = m₃x + c₃ are concurrent, then show that m₁(c₂ – c₃) + m₂(c₃ – c₁) + m₃(c₁ – c₂) = 0.

Q.9 Find the equation of a line which is equidistant from the lines x = - 4 and x = 8.

Q.10 The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.

Q.11 Find the value of p so that the three lines 3x + y - 2 = 0, px + 2y - 3 = 0 and 2x - y - 3 = 0 may intersect at one point.

Q.12 Reduce 4x – 3y -12 = 0 to the ‘intercept form''.

Q.13 Find the equation of the line perpendicular to the line 2x – 3y + 7 = 0 and having x-intercept 4.

Q.14 By using the concept of equation of a line, prove that the three points (3, 0), (–2, –2) and (8, 2) are collinear.

Q.15 Find the equation of the right bisector of the line segment joining the points (3, 4) and (–1, 2).

Q.16 Find the equation of the straight line passing through (2, 3) and cutting off intercepts equal in magnitude and opposite in sign.

Q.17 Prove that the product of the lengths of the perpendiculars drawn from the points (√a² - b², 0) and ( - √a² - b², 0) to the line x/a cos θ + y/b sin θ = 1 is b^{2 .}

Q.18 Find equation of the line perpendicular to the line x – 7y + 5 = 0 and having x intercept 3.

Q.19 A line passes through (x₁, y₁) and (h, k). If slope of the line is m, show that k - y₁ = m(h – x₁).

Q.20 Write the equation of a line passing through (2,3) and makes an angle of 45° with x-axis.