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EXERCISE – 14

Q. 1.. A line joining A(4, 5) and B(1, 2) is parallel to the joining C(1, -2) and D(0, k). Find the value of k.

Q. 2. Find the equation of the line joining the points (-4, -6), (3, 1).

Q. 3. Find the equation of a straight line passing through the point (2, 5) and perpendicular to the line 3x + 4y + 7 = 0.

Q. 4. Find the equation of the line through (0, 1) and equally inclined to the axes in the 2nd quadrant

Q. 5. Find the equation of the line passing through the intersection of 2x – y = 1 and 3x + 2y + 9 = 0 and having slope equal to 1.

Q. 6. he co-ordinates of two points A and B are (0, 4) and (3, 7) respectively. Find

1. The gradiant of AB.
2. The equation of AB.
3. The co-ordinates of the point where the line AB intersects the x-axis.

Q. 7. P, Q, R have co-ordinates (-2, 1), (2, 2) and (6, -2) respectively. Write down

1. The gradient of QR
2. The equation of the line through P perpendicular to QR.

Q. 8. Write down the equation of the line parallel to x – 2y + 8 = 0 and passing through the point (1, 2).

Q.9. Given that the line y/2 = x – p and the line ax + 5 = 3y are parallel, find the value of a.

Q.10. Find the equation of the line through (1, 3) making an intercept of 5 on the y-axis.

Q.11. In the figure alongside, the lines are represented. Write down the angles that the lines make with the position direction of the x-axis. Hence determine angle .

Q.12. Find the equation of the perpendicular dropped from (-1, 2) on the line joined (1, 4) and (2, 3).

Q.13. (i) Write down the equation of the line AB through (3, 2) and perpendicular to the line 2y = 3x + 5.

(ii) AB meets the x-axis at A and y-axis at B. Writ down the co-ordinates of A and B. Calculate area of the triangle OAB, where O is the origin.

Q.14. A (2, -4), B (3, 3) and C (-1, 5) are the vertices of the triangle ABC. Find the equation of

1. The median of the triangle through A.
2. The attitude of the triangle through B.

Q. 15. Find the equation of a line, which has y-intercept 4 and which is parallel to the line 2x – 3y = 7. Find the co-ordinates of the point, where it cuts the x-axis.

Q. 16. (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.

Q.17. Find the equation of the line which is parallel to 3x – 2y = -4 and passes through the point (0, 3).

Q.18. Find the equation of the straight line which passes through the point of intersection of the two lines 2x – y + 5 = 0 ; 5x + 3y – 4 = 0 and is perpendicular to the line x – 3y + 21 = 0

Q.19. Find the equation of the line passing through (0, 4) and parallel to the line 3x + 5y + 15 = 0.

Q.20. ABCD is a rhombus. The co-ordinates of A and C are (3, 6) and (-1, 2) respectively. Write down the equation of BD.

Q.21. Write down the equation of the line whose gradient is 3/2 and which passes through P. Where P divides the line segment joining A(-2, 6) and B(3, -4) in the ratio 2 : 3.

Q.22. A(1, 4), B(3, 2) and C(7, 5) are the vertices of a triangle ABC. Find

1. The co-ordinates of the centroid G of
2. The equation of a line through G and parallel to AB.

Q.23. If the line y = 3x + 7 and 2y + px = 3 are perpendicular to each other, find the value of p.

Answers
1. k = 3	2. y = x - 2
3. 3x + 4y – 26 = 0	4. y = x + 1
5. y = x - 2	6. (i) 1 (ii) y = x + 4 (iii) (-4, 0)
7. (i) -1 (ii) y = x + 3	8. x – 2y + 3 = 0
9. a = 6	10. 2x + y = 5
11.	12. y = x + 3
13. (i) 2x + 3y – 12 = 0 (ii) A(6, 0), B(0, 4)	14. (i) 8x + y = 12 (ii) x – 3y + 6 = 0
15. 3y = 2x + 14 ; (-6, 0)	16. (i) A(-3. 0) (ii) 4y = -3x – 9
17. 2y = 3x + 6	18. 3x + y = 0
19. 3x + 5y = 20	20. x + y - 5 = 0
21. 3x – 2y + 4 = 0	22. (i) (11/3, 11/3) (ii) 3x + 3y – 22 = 0
23. p = 2/3