A straight line L1 has a gradient ˉ½ and passes through point P (1, 3). Another line L2 passes through the points Q (1, 3) and R (4, 5). Find.(a) The equation of L1. (2mks)(b) The gradient of L2. (1mk)
(c) The equation of L2. (2mks)(d) The equation of a line passing through a point S (0, 5) and is perpendicular to L2. (3mks)(e) The equation of a line through R parallel to L1. (2mks)
A line passes through the point (1, 2) and has gradient ½. Write down its equation in the form ax + by = c (3mks)The gradient of a line L through points A(2x, 4) and B(1, x) is 1/7. find the equation of a line perpendicular to L through B (3mks)
Worked Answer:
Form 2 Mathematics
(a) A line, L1, posies through tho points (3,3) and (5,7). Find the equation of L1, in the form y = mx+c where m and c arc constonti.
(b) Another line L2 is perpendicular to L1, and passes through (2, 3). Find: (i) the equation of L2; (ii) the xintercept of L2. (c) Determine the point of intersection of L1, and L2. Form 2 Mathematics
Two vertices of a triangle ABC are A (3,6) and B (7,12).
(a) Find the equation of line AB. (b) Find the equation of the perpendicular bisector of line AB. (c) Given that AC is perpendicular to AB and the equation of line BC is y = 5x + 47, find the coordinates of C. Form 2 Mathematics
Two lines L1: 2y — 3x 6 = 0 and L2: 3y + x — 20 = 0 intersect at a point A.
(a) Find the coordinates of A. (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. (c) Another line L4 is parallel to L1 and passes through (—1,3). Find the x and y intercepts of L4 Form 2 Mathematics
A line L is perpendicular to the line 2⁄3x + 5⁄7 y = 1 . Given that L passes through (4,11), find:
(a) gradient of L1 (b) equation of L in the form y = mx + c, where m and c are constants. Form 2 Mathematics
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 constant Form 2 Mathematics
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.
Form 2 Mathematics
(a) A straight line L, whose equation is 3y — 2x = —2 meets the xaxis at R.
Determine the coordinates of R. b) A second line L2 is perpendicular to L1 at R. Find the equation of L2 in the form y = mx + c, where m and c are constants. (c) A third line L3 passes through (—4,1) and is parallel to L2 Find: (i) the equation of L3 in the form y = mx + c, where m and c are constants (ii) the coordinates of point S, at which L intersects L Form 2 Mathematics
A line L passes through (2, 3) and (1, 6) and is perpendicular to a line P at (1, 6).
(a) Find the equation of L (b) Find the equation of P in the form ax + by = c,where a, b and c are constants. (c) Given that another line Q is parallel to L and passes through point (1, 2) find the x and y intercepts of Q (d) Find the point of the intersection of lines P and Q Form 2 Mathematics
A straight line passes through points (2, 1) and (6, 3).
Find: a) equation of the line in the form y = mx + c; b) the gradient of a line perpendicular to the line in (a) Form 2 Mathematics
A line L passes through point (3,1) and is perpendicular to the line 2y = 4x + 5.
Determine the equation of line L. Form 2 Mathematics
A straight line l passes through the point (3, —2) and is perpendicular to a line whose equation is 2y4x= 1.
Find the equation of l in the form y = mx + c, where m and c are constants. Form 2 Mathematics
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. 
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