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Past KCSE Mathematics Questions and Video Answers on Equations of Straight Lines
Determine if the line 6(x-3y)+7=0 and the line through the origin having gradient -3 are parallel.
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1.
Two vertices of a triangle ABC are A (3, 6) and B (7,12).(a) Find the equation of line AB. (3 marks) (b) Find the equation of the perpendicular bisector of line AB. (4 marks) (c) Given that AC is perpendicular to AB and the equation of line BC is y = -5x + 47, find the co-ordinates of C. (3 marks)
2.
Two lines L1: 2y - 3x - 6 = 0 and L2: 3y + x - 20 = 0 intersect at a point A. (a) Find the coordinates of A. (3 marks) (b) A third line L3 is perpendicular to L2 at point A. Find the equation of L3 in the form y = mx + c, Where m and c are constants. (3 marks) (c) Another line L4 is parallel to L1 and passes through (-l, 3). Find the x and y intercepts of L 4 (4 marks)
3.
A line L is perpendicular to the line #(2)/(3)x + (5)/(7)y=1# Given that L passes through (4, l l), Fnd: (a) Gradient of #L_1# (l mark) (b) Equation of L in the form y = mx + c, where m and c are constants. (2 marks)
4.
A line with gradient of -3 passes through the points (3, k) and (k, 8). Find the value of k and hence express the equation of the line in the form ax + by = c, where a, b and c are constants. (3 marks)
5.
a).A straight line L1 whose equation is 3y -2x = -2 meets the x-axis at R. Determine the co-ordinates of R. (2 marks) (b) A second line L2 is perpendicular to L] at R. Find the equation of L2 in the form y = mx + c, where m and c are constants. (3 marks) (c) A third line L3 passes through (-4, 1) and is parallel to Ll. Find: (i) The equation of L3 in the form y = mx + c, where m and c are
6.
KCSE 2014 paper 1 question 17. A line L passes through points (- 2. 3) and (- 1, 6) and is perpendicular to a line P at (-1,6). (a) Find the equation of L. (2 marks) (b) Find the equation of P in the form ax + by = c, where a, b and c are constants. (2 marks) (c) Given that another line Q is parallel to L and passes through point (1, 2), find the x and y intercepts of Q. (3 marks)
7.
A straight line passes through points (-2, 1) and (6, 3). Find: (a) The equation of the line in the form y =mx +c. (b).The gradient of a line perpendicular to the line in (a).
8.
A line L passes through point (3,1) and is perpendicular to the line 2y =4x +5.Determine the equation of the line L.
9.
A straight line L passes through the points (3,-2) and is perpendicular to a line whose equation is 2y- 4x =1.Find the equation of L in the form y =mx +c where m and c are constants.
10.
A line which joins the points A (3,k) and B(-2,5) is parallel to another line whose equation is 5y +2x =10.Find the value of k.
11.
Three vertices of a rhombus ABCD are: A (-4,-3),B(1,-1) and C(3,4). a).Draw the rhombus. b).Find the equation of the line AD in the form y =mx +c, where m and c are constants.
12.
The equation of the line L1 is 2y – 5x -8 =0 and line L2, passes through the points (-5, 0) and (5,-4).Without drawing the line L1 and L2 show that the two lines are perpendicular to each other
13.
Find the equation of a line which equidistant from the points (2, 3) and (6, 1) expressing it in the form ax +by = c where a, b and c are constants.
14.
A perpendicular to the line y- 4x+3 = 0 passes through point (-8,5).Determine its equation
15.
Two lines L1 and L2 intersect at a point P.L1 passes through the points (-4,0) and (0,6).Given that L2 has the equation: y=2x-2,find,by calculation, the coordinates of P.
16.
P (5,-4) and Q(-1,-2) are points on a straight line. Find the equation of the perpendicular bisector of PQ; giving the answer in the form y=mx+c.
17.
A straight line passes through points A (-3,8) and B(3,-4).Find the equation of the straight line through (3,4) and parallel to AB. Give your answer in the form y=mx + c, where m and c are constants.
18.
A line L1 passes through point (1, 2) and has a gradient of 5.Another line L2, is perpendicular to L1 and meets it at a point where x=4.find the equation of L2 in the form y=mx +c.
19.
Find the equation of a line perpendicular to the line x+2y =4 and passes through point (2,1).
20.
The equation of a line is # (-3)/ 5 x + 3y =6 #.Find the: a).Gradient of the line. b).Equation of the line passing through point (1, 2) and perpendicular to the given line.
21.
Determine which of the following pairs of straight lines are parallel. Do not draw the lines. a) y=#1/2x+7# #y=1/2x-20# b) #3/2x+2/3y+3/2=0# # 2/3x+3/2y+2/3=0# c) 2x+3y-8=0 21-4x-6y=0
22.
Determine which of the following pairs of straight lines are parallel. Do not draw the lines. a) 5x+6y-4=0 #y=6/5x+2/3# b) 2y-7x-8=0 4y+17=14x c) #y=-4/5 x+13# and the line through (-1,-3) and (-3.5,-11)
23.
Determine if the line 6(x-3y)+7=0 and the line through the origin having gradient -3 are parallel.
24.
Determine if a line through (0,7) and (1,11) and another line through (1, 11.8) and (2,14.6) are parallel.
25.
Determine if a line through (1,4) and (-1,1) and another line through (99,103) and (51,7) are parallel.
26.
In each of the following, find the equation of the line through the given point and parallel to the given line: a) (0, 0); y = #2/7#x + 1 b) (3.5, 0); x+y = 10
27.
In each of the following, find the equation of the line through the given point and parallel to the given line: a) (5, 2); 5y - #2/7#x – 115=0 b) (-3, 5); 7y = 3x
28.
In each of the following, find the equation of the line through the given point and parallel to the given line: a) (0, -3); 2x+y= -3 b) (2,3); y = 0
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