Coordinate Geometry Mathematic
 |
| Coordinate Geometry Mathematic |
Important information:- It is a system of geometry, where the position of points on the plane is described by using an ordered pair of numbers.
#Rectangular Coordinate Axes :- The lines XOX' and YOY' are mutually perpendicular to each other and they meet at point O which is called the origin.
Quadrants:- The X and Y-axes divide the cartesian plane into four regions referred to quadrants
Table of Contain:-
(a) 1st
(b) 2nd
(c) 3rd
(d) 4th
Answer :- (b) 2nd
2. On which axis does the point (6, 0) lie?
(a) x-axis
(b) y-axis
(c) Either x or y
(d) At origin
(e) None of the above
Answer :- (a) x-axis
3. The distance of the point P (8, - 6) from the origin is
(a) 2 units
(b) 8 units
(c) 10 units
(d) 16 units
(e) None of the above
Answer :- (c) 10 units
4. If the distance between the points (x, 0) and (-7, 0) be 10 units, then the possible values of x are ?
(a) 3 and 17
(b)-3 and 17
(c) 3 and -17
(d) -3 and -17
Answer :- (c) 3 and -17
5. If the distance of the point P (x, y) from A(a, 0) is a + x, then y 2 = ?
(a) 2ax
(b) 4ax
(c) 6ax
(d) 8ax
(e) None of the above
Answer :- (b) 4ax
6. The intersection point on the x-axis of 7x - 3y = 2 is ?
(a) 2/5
(b) 2/7
(c) 3/4
(d) 3/7
Answer :- (b) 2/7
7. Locus of the points equidistant from the points (- 1,-1) and (4, 2) is
(a) 5x - 3y - 9 = 0
(b) 5x + 3y + 9 = 0
(c) 5x + 3y - 9 = 0
(d) 5x - 3y + 9 = 0
(e) None of the above
Answer :- (c) 5x + 3y - 9 = 0
8. Coordinates of a point is (0, 1) and ordinate of an another point is - 3. If distance between both the points is 5, then abscissa of second point is
(a) 3
(b) -3
(c) ±3
(d) 1
(e) -1 9.
Answer :- (c) ±3
9. The vertices of a triangle are A (4, 4), B 3,- 2 and C (- 3,16). The area of the triangle is
(a) 30 sq units
(b) 36 sq units
(c) 27 sq units
(d) 40 sq units
(e) None of the above
Answer :- (c) 27 sq units
10. Two vertices of an equilateral triangle are origin and (4, 0). What is the area of the triangle?
(a) 4 sq units
(b) 3 sq units
(c) 4✓3 sq units
(d) 2✓3 sq units
(e) 5✓3 sq units
Answer :- (c) 4✓3 sq units
11. If the points A 1,-1 B 5, 2 and C k &,5 are collinear, then k = ?
(a) 2
(b) 4
(c) 6
(d) 9
(e) None of the above
Answer :- (d) 9
12. Slope of x-axis is
(a) 0
(b) 1
(c) -1
(d) ~
(e) None of the above
Answer :- (a) 0
13. Slope of y-axis is
(a) 0
(b) 1
(c) -1
(d) ~
(e) None of the above
Answer :- (d) ~
14. If two vertices of a triangle are (5, 4) and (-2, 4) and centroid is (5, 6), then third vertex is
(a) (12,10)
(b) (10,12)
(c) (-10,12)
(d) (12,-10)
(e) (-10,-12)
Answer :- (a) (12,10)
15. The points (2, 2) (6, 3) and (4, 11) are the vertices of
(a) an equilateral
(b) a right angled triangle
(c) an isosceles triangle
(d) a scalene triangle
(e) do not form triangle
Answer :- (b) a right angled triangle
16. A point C divides the line AC, where A(l, 3) and B (2, 7) in the ratio of 3 : 4. The coordinates of C are ?
(a) (5/3 , 5)
(b) (3/5 , 5)
(c) (-2 , -9)
(d) (10/7 , 33/7)
Answer :- (d) (10/7 , 33/7)
17. The slope of a line passing through the points A (4, - 3) and B (6, - 3) is
(a) 4
(b) 0
(c) -
(d) 5
(e) None of the above
Answer :- (b) 0
18. If the inclination of a line joining the points A (x, - 3) and B (2, 5) is 135°, then z=?
(a) 10
(b) 15
(c) 20
(d) 25
(e) None of the above
Answer :- (a) 10
19. If a point (x, y) in a OXY-plane is equidistant from (-1,1) and (4, 3), then [CLAT2013] ?
(a) 10x + 4y = 23
(b) 6x + 4y = 23
(c) -x +y = 7
(d) 4x+3y=0
Answer :- (a) 10x + 4y = 23
20. If the graph of the equation 2x+ 3y = 6 form a triangle with coordinates axis, then the area of triangle will be [SSC (10+2) 2012]
(a) 2 sq units
(b) 3 sq units
(c) 6 sq units
(d) 1 sq units
Answer :- (b) 3 sq units
21. If A -5, 7) B -4,-5) C-1,-6) and Z) (4,5) are the vertices of a quadrilateral, then find the area of the quadrilateral ABCD.
(a) 72 sq units
(b) 80 sq units
(c) 90 sq units
(d) 92 sq units
(e) None of the above
Answer :- (a) 72 sq units
22. Find the equation of a line parallel to y-axis and passing through the point (- 3, 4)
(a) x + 3 = 0
(b) x - 3 = 0
(c) x + 4 = 0
(d) x - 4 = 0
(e) None of the above
Answer :- (a) x + 3 = 0
23. Find the equation of a line of unit slope and passing through the origin.
(a) y = x
(b) x + y = 0
(c) x = y + 1
(d) x = 1/2y +1
Answer :- (a) y = x
24. The value of k for which the lines x + 1y = 9 and kx + 4y = - 5 are parallel, is
(a) k = 2
(b) k = 1
(c) k = - 1
(d) k = 3
(e) None of the above
Answer :- (a) k = 2
25. Find the value of k for which the lines 5x + 3y + 2 = 0 and 3x - ky + 6 = 0 are perpendicular.
(a) 5
(b) 4
(c) 3
(d) 2
(e) 1
Answer :- (a) 5
26. The length of the equation 4x+ 3y - 12 = 0 that intersects two coordinate axes is
(a) 2.5 units
(b) 7 units
(c) 5 units
(d) 6 units
Answer :- (c) 5 units
27. Find the distance of the intercept at point of x-axis and the line 5x+ 9y - 45 from origin.
(a) 5
(b) 9
(c) 5/9
(d) 9/5
(e) None of the above
Answer :- (b) 9
28. Find the equation of perpendicular bisector of the line made by joining the points (1, 1)
and (3, 5).
(a) x + 2y + 8 = 0
(b) x - 2y + 8 = 0
(c) x - 2y - 8 = 0
(d) x + 2y - 8 = 0
(e) None of the above
Answer :- (d) x + 2y - 8 = 0
29. Find the equation of the line which makes equal intercepts on the axis and passes through the point (4, 5).
(a) x+ y = 9
(b) x+2y = 7
(c) 2x+2y = 7
(d) 2x + y = 7
Answer :- (a) x+ y = 9
30. In what ratio, the line made by joining the points A (- 4,- 3) and B (5,2) intersects x-axis?
(a) 3 : 2
(b) 2 : 3
(c) -3 : 2
(d) -2:3
(e) None of the above
Answer :- (a) 3 : 2
31. Find the ratio in which the line 3x + y - 9 divides the line made by joining the points (1, 3) and (2, 7).
(a) 3:4 external
(b) 3:4 internal
(c) 1 : 4 internal
(d) 4:3 internal
(e) None of the above
Answer :- (b) 3:4 internal
32. If the point (x, y) is equidistant from points (7, 1) and (3, 5), find (x - y).
(a) 2
(b) 4
(c) 6
(d) 8
(e) None of the above
Answer :- (a) 2
33. The area of the region bounded by y = |x| - 5 with the coordinate axis is [SSCCGL2012]
(a) 25 sq units
(b) 52 sq units
(c) 50 sq units
(d) 20 sq units
Answer :- (a) 25 sq units
34. If three vertices of a parallelogram are A (3,5) £(-5,-4) and C(7, 10), then fourth vertex is
(a) (10,19)
(b) (15,10)
(c) (19,10)
(d) (10,15)
(e) (15,19)
Answer :- (e) (15,19)
35. Three vertices of a rhombus are (2,-1), (3, 4) and (-2, 3). Find the fourth vertex.
(a) (1,2)
(b) (3,2)
(c) (-2,-3)
(d) (-3,-2)
(e) (2,3)
Answer :- (d) (-3,-2)
36. Do the points (4, 3), (- 4,- 6) and (7, 9) form a triangle ? If yes, then find the longest side of the triangle.
(a) 18.6
(b) 16.5
(c) 24
(d) 34
(e) Triangle can't be formed
Answer :- (a) 18.6
37. Are the points (1, 7), (4, 2), (- 1,- 1) and (- 4, 4) vertices of a square? If yes, what is the length of the side of square?
(a) 34
(b) √34
(c) 25
(d) √25
(e) None of the above
Answer :- (b) √34
38. If the points A (6, 1), B(8, 2), C(9, 4) and D(P,3) are the vertices of a parallelogram, taken in order, find the value of P.
(a) 3
(b) 4
(c) 5
(d) 6
(e) 7
Answer :- (e) 7
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