Class X ICSE Maths Chapter Equation Of Line Exercise 12.2
Welcome to our extensive collection of questions on the topic "Equation of a Line," crafted to help you master this fundamental concept in coordinate geometry. Our question bank covers key aspects such as slope-intercept form, point-slope form, general form, and finding equations of parallel and perpendicular lines. These questions are ideal for students aiming to strengthen their understanding of line equations and their applications in solving real-world problems. Whether you're preparing for exams or simply improving your geometry skills, our resource provides the perfect platform to practice and excel in the "Equation of a Line."
Select Exercise
Q1 State which one of the following is true : The straight lines y = 3x - 5 and 2y = 4x + 7 are
(i) parallel
(ii) perpendicular
(iii) neither parallel nor perpendicular.
Q3 Lines 2x - by + 5 = 0 and ax + 3y = 2 are parallel. Find the relation connecting a and b.
Q4 If the straight lines 3x - 5y = 7 and 4x + ay + 9 = O are perpendicular to one another, find the value of a
Q5 If the lines 3x + by + 5 = 0 and ax - 5y + 7 = 0 are perpendicular to each other, find the relation connecting a and b.
Q6 Is the line through ( - 2, 3) and (4, 1) perpendicular to the line 3x = y + 1 ?
Does the line 3x = y + 1 bisect the join of ( - 2, 3) and (4, 1).
Q7 The line through A ( - 2, 3) and B (4, b) is perpendicular to the line 2x - 4y = 5. Find the value of b.
Q8 If the lines 3x + y = 4, x - ay + 7 = 0 and bx + 2y + 5 = 0 form three consecutive sides of a rectangle, find the value of a and b.
Q9 Find the equation of a line, which has the y-intercept 4, and is parallel to the line 2x - 3y - 7 = 0. Find the coordinates of the point where it cuts the x-axis.
Q10 Find the equation of a straight line perpendicular to the line 2x + 5y + 7 = 0 and with y-intercept - 3
Q11 Find the equation of a straight. line perpendicular to the line 3x - 4y + 12 = 0 and having same y-intercept as 2x - y + 5 = 0.
Q12 Find the equation of the line passing through (0, 4) and parallel to the line 3x + 5y + 15 = 0.
Q13 Write down the equation of the line perpendicular to 3x + 8y = 12 and passing through the point ( - 1, - 2).
Q14 (i) The line 4x - 3y + 12 = 0 meets the x-axis at A. Write down the co-ordinates of A.
(ii) Determine the equation of the line passing through A and perpendicular to 4x - 3y + 12 = 0.
Q15 Find the equation of the line that is parallel to 2x + 5y - 7 = 0 and passes through the mid-point of the line segment joining the points (2, 7) and ( - 4, 1).
Q16 Find the equation of the line that is perpendicular to 3x + 2y - 8 = 0 and passes through the mid-point of the line segment joining the points (5, - 2), (2, 2).
Q17 Find the equation of a straight line passing through the intersection of 2x + 5y - 4 = 0 with x-axis and parallel to the line 3x - 7y + 8 = 0.
Q18 The equation of a line is 3x + 4y - 7 = 0. Find
(i) the slope of the line. .
(ii) the equation of a line perpendicular to the given line and passing through the intersection of the lines x - y + 2 = 0 and 3x + y - 10 = 0.
Q19 Find the equation of the line perpendicular from the point (1, - 2) on the line 4x - 3y - 5 = 0. Also find the co-ordinates of the foot of perpendicular.
Q20 Prove that the line through (0, 0) and (2, 3) is parallel to the line through (2, - 2) and (6, 4).
Q21 Prove that the line through,( - 2, 6) and (4, 8) is perpendicular to the line through (8, 12) and (4, 24).
Q22 Show that the triangle formed by the points A (1, 3), B (3, - 1) and C ( - 5, - 5) is a right angled triangle by using slopes.
Q23 Find the equation of the line through the point ( - 1, 3) and parallel to the line joining the points (0, - 2) and (4, 5).
Q24 A ( - 1, 3), B (4, 2), C (3, - 2) are the vertices of a triangle.
(i) Find the coordinates of the centroid G of the triangle.
(ii) Find the equation of the line through G and parallel to AC
Q25 Find the equation of the line through (0, - 3) and perpendicular to the line joining the points (- 3, 2) and (9, 1).
Q26 The vertices of a ∆ABC are A(3, 8), B(-1, 2) and C(6, -6). Find :
(i) Slope of BC.
(ii) Equation of a line perpendicular to BC and passing through A
Q27 The vertices of a triangle are A (10, 4), B (4, - 9) and C ( - 2, - 1). Find the equation of the altitude through A.
Q28 A (2, - 4), B (3, 3) and C ( - 1, 5) are the vertices of triangle ABC. Find the equation of :
(i) the median of the triangle through A
(ii) the altitude of the triangle through B
Q29 Find the equation of the right bisector of the line segment joining the points (1, 2) and (5, - 6).
Q30 Points A and B have coordinates (7, - 3) and (1, 9) respectively. Find
(i) the slope of AB.
(ii) the equation of the perpendicular bisector of the line segment AB.
(iii) the value of ‘p’ if ( - 2, p) lies on it.
Q31 The points B (1, 3) and D (6, 8) are two opposite vertices of a square ABCD. Find the equation of the diagonal AC.
Q32 ABCD is a rhombus. The co-ordinates of A and C are (3, 6) and ( - 1, 2) respectively. Write down the equation of BD.
Q34 If the line x - 4y - 6 = 0 is the perpendicular bisector of the line segment PQ and the co-ordinates of P are (1, 3), find the co-ordinates of Q.
Q35 OABC is a square, O is the origin and the points A and B are (3, 0) and (p, q). If OABC lies in the first quadrant, find the values of p and q. Also write down the equations of AB and BC.
Add a comment