EQUATION OF STRAIGHT LINE WORKSHEET FOR GRADE 11

(1)  Show that the lines are 3x + 2y + 9 = 0 and 12x + 8y − 15 = 0 are parallel lines.     Solution

(2)  Find the equation of the straight line parallel to 5x − 4y+3 = 0 and having x-intercept 3.     Solution

(3)  Find the distance between the line 4x + 3y + 4 = 0, and a point (i) (−2, 4) (ii) (7,−3)       Solution

(4)  Write the equation of the lines through the point (1,−1)

(i) parallel to x + 3y − 4 = 0

(ii) perpendicular to 3x + 4y = 6     Solution

(5)  If (−4, 7) is one vertex of a rhombus and if the equation of one diagonal is 5x − y + 7 = 0, then find the equation of another diagonal.           Solution

(6)  Find the equation of the lines passing through the point of intersection lines 4x − y + 3 = 0 and 5x + 2y + 7 = 0, and (i) through the point (−1, 2) (ii) Parallel to x−y+5 = 0 (iii) Perpendicular to x − 2y + 1 = 0         Solution

(7)  Find the equations of two straight lines which are parallel to the line 12x + 5y +2 = 0 and at a unit distance from the point (1, − 1).              Solution

(8)  Find the equations of straight lines which are perpendicular to the line 3x+ 4y −6 = 0 and are at a distance of 4 units from (2, 1).      Solution

(9)  Find the equation of a straight line parallel to 2x + 3y = 10 and which is such that the sum of its intercepts on the axes is 15           Solution

(10)  Find the length of the perpendicular and the co-ordinates of the foot of the perpendicular from (−10,−2) to the line x + y − 2 = 0          Solution

(11)  If p₁ and p₂ are the lengths of the perpendiculars from the origin to the straight lines x sec θ + y cosec θ = 2a and x cos θ − y sin θ = a cos 2θ, then prove that p₁²+ p₂²= a².          Solution

(12)  Find the distance between the parallel lines

(i) 12x + 5y = 7 and 12x + 5y+7 = 0

(ii) 3x − 4y + 5 = 0 and 6x − 8y − 15 = 0.          Solution

(13)  Find the family of straight lines (i) Perpendicular (ii) Parallel to 3x + 4y − 12 = 0.           Solution

(14)  If the line joining two points A(2,0) and B(3,1) is rotated about A in anticlockwise direction through an angle of 15°, then find the equation of the line in new position.            Solution

(15)  A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and it passes through the point (5,3). Find the co-ordinates of the point A.    Solution 

(16)  A line is drawn perpendicular to 5x = y + 7. Find the equation of the line if the area of the triangle formed by this line with co-ordinate axes is 10 sq. units.     Solution

(17)  Find the image of the point (−2, 3) about the line x + 2y − 9 = 0.      Solution

(18)  A photocopy store charges Rs. 1.50 per copy for the first 10 copies and Rs. 1.00 per copy after the 10th copy. Let x be the number of copies, and let y be the total cost of photocopying. (i) Draw graph of the cost as x goes from 0 to 50 copies. (ii) Find the cost of making 40 copies    Solution

(19)  Find atleast two equations of the straight lines in the family of the lines y = 5x + b, for which b and the x-coordinate of the point of intersection of the lines with 3x − 4y = 6 are integers    Solution

(20)  Find all the equations of the straight lines in the family of the lines y = mx − 3, for which m and the x-coordinate of the point of intersection of the lines with x − y = 6 are integers.       Solution

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