**KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed**

Comprehensive Answers and Marking Schemes KNEC Certified

Comprehensive Answers and Marking Schemes KNEC Certified

## QUESTION 19 | KCSE 2022 | EQUATIONS OF A STRAIGHT LINE | PAPER 1 | FORM 2 LEVELA triangle ABC is right angled at point A. The vertices of the triangle are A(1, -2), B(5, 4) and C(m, n).
The equation of line BC is 5y - x = 15. - (a) Determine:
- (i) the equation of line AC in the form ax + by + c = 0, where a, b and c are integers.
**(4 marks)** - (ii) the coordinates of point C.
**(3 marks)**
- (i) the equation of line AC in the form ax + by + c = 0, where a, b and c are integers.
- (b) A line passes through point A and is parallel to line BC.
Determine the x-intercept of the line.**(3 marks)**
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## 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(b) Another line L2 is perpendicular to L1, and passes through (-2, 3). Find: (i) the equation of L2; (ii) the x-intercept of L2. (c) Determine the point of intersection of L1, and L2. ## Form 2 Mathematics(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(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) gradient of L1 (b) equation of L in the form y = mx + c, where m and c are constants. ## Form 2 Mathematicswhere a, b and c are constant ## Form 2 Mathematics## Form 2 MathematicsDetermine the co-ordinates 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 co-ordinates of point S, at which L intersects L ## Form 2 Mathematics(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 MathematicsFind: 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 MathematicsDetermine the equation of line L. ## Form 2 MathematicsFind the equation of l in the form y = mx + c, where m and c are constants. ## Form 2 MathematicsFind the value of k. ## Form 2 Mathematics## Form 2 Mathematicsa) Draw the rhombus on the grid provided below. b) Find the equation of the line AD in the form y = mx + c, where and c are constants. ## Form 2 Mathematics## Form 2 Mathematics## Form 2 Mathematics
## Form 2 Mathematics
Find equation of the perpendicular to the line x + 2y – 4 and passes through point (2,1)
## Form 2 Mathematics
The equation of a line is
\[-\frac{3}{5}x + 3y = 6\]
Find the:
- (a) Gradient of the line
- (b) Equation of a line passing through point (1,2) and perpendicular to the given line.
## Related Questions## The data given below represents the average monthly expenditure, E in K £, on food in a certain village. The expenditure varies with number of dependents, D in the family## (a) Using the grid provided, plot E against D and draw the line of the best fit |

## A perpendicular to the line -4x + 3 = 0 passes through the point (8,5). Determine its equation. |