SAMACHEER KALVI CLASS 10 ASSIGNMENT 3 - SUMS IN COORDINATE GEOMETRY

SAMACHEER KALVI

CLASS 10

ASSIGNMENT 3

COORDINATE GEOMETRY


1. Find the area of the triangle formed by the points:


(i) (1,-1), (-4, 6) and (-3, -5)


2. Find the value of ‘a’ for which the given points are collinear.

(i) (2,3), (4, a) and (6, -3)

3. Determine whether the sets of points are collinear?

(i) (a, b+c), (b, c+a) and (c, a+b)

4. Find the area of the quadrilateral whose vertices are at

(i) (-9, 0), (-8,6), (-1, -2) and (-6, -3)

5. What is the slope of a line perpendicular to the line joining A(5,1) and P where P is the mid-point of the segment joining (4,2) and (-6,4).


6. If the three points (3, -1), (a, 3) and (1, -3) are collinear, find the value of a.


7. What is the inclination of a line whose slope is 0 ?


8. What is the slope of a line whose inclination with positive direction of x -axis is 90° ?


9. The line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8,12) and (x, 24). Find the value of x.


10. Show that the given points form a right angled triangle and check whether they satisfy Pythagoras theorem.
  L(0, 5), M(9,12) and N(3,14)


11. If the points A(2, 2), B(-2, -3), C(1, -3) and D(x, y) form a parallelogram then find the value of x and y.


12. Find the equation of a straight line passing through the mid-point of a line segment joining the points (1, -5), (4, 2) and parallel to (i) X axis (ii) Y axis.

13. Find the value of ‘a’, if the line through (-2,3) and (8,5) is perpendicular to y = a x + 2.

14. Find the equation of a line through the given pair of points:
 2 (2,3) and (-7,-1)

15. Find the value of k, if the area of a quadrilateral is 28 sq. units, whose vertices are (-4, -2), (-3, k), (3, -2) and (2, 3).


16. If the points A(-3, 9), B(a, b) and C(4, -5) are collinear and if a + b = 1, then find a and b.


17. Find the equation of a straight line which has slope  

−54 and passing through the point (-1,2).


18. Find the slope of the straight line 5y – 3 = 0.


19. Check whether the given lines are parallel or perpendicular:

 5x + 23y + 14 = 0 and 23x – 5x + 9 = 0


20. Find the equation of a straight line passing through the point P(-5,2) and parallel to the line joining the points Q(3, -2) and R(-5,4).


21. Find the equation of a line passing through (6, -2) and perpendicular to the line joining the points (6, 7) and (2, -3).


22. Find the equation of a straight line through the intersection of lines 7x + 3y = 10, 5x – 4y = 1 and parallel to the line 13x + 5y + 12 = 0.


23. The area of a triangle is 5 sq. units. Two of its vertices are (2,1) and (3, -2). The third vertex is (x, y) where y = x + 3 . Find the coordinates of the third vertex.
 


24. Without using distance formula, show that the points (-2,-1), (4,0), (3,3) and (-3,2) are vertices of a parallelogram.


25. Find the image of the point (3,8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror. 


26. Find the equation of a line passing through the point of intersection of the lines 4x + 7y – 3 = O and 2x – 3y + 1 = 0 that has equal intercepts on the axes.
 

27. Find the area of a triangle formed by the lines 3x + y – 2 = 0, 5x + 2y – 3 = 0 and 2x – y – 3 = 0
 

28. The slope of the line joining (12, 3), (4, a) is 

18. Find the value of a .






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