Coordinate geometry is a branch of mathematics that uses coordinate points to study geometry. It's a fundamental part of mathematics that provides a relationship between algebra and geometry through graphs of lines and curves.  In coordinate geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of points or other geometric elements on a manifold such as Euclidean space. Here are some examples of coordinate geometry: Coordinate plane: A grid system created by the intersection of two number lines called axes. The... Show more

Coordinate geometry is a branch of mathematics that uses coordinate points to study geometry. It's a fundamental part of mathematics that provides a relationship between algebra and geometry through graphs of lines and curves. 

In coordinate geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of points or other geometric elements on a manifold such as Euclidean space.

Here are some examples of coordinate geometry:
Coordinate plane: A grid system created by the intersection of two number lines called axes. The horizontal number line is the x-axis, and the vertical number line is the y-axis. The point where the both meet is known as the origin, which has the (x, y) coordinates (0, 0).
Section formula: Helps us knowing the coordinates of the points that are dividing a given line segment into two parts. The section formula is useful to find the coordinates of a point that divides the line segment joining the points (x1,y1) and (x2,y2) in the ratio m:n.
Straight line equation: The equation is y = mx + c, where m is the slope and c tan θ = m, where x is the positive axis.

Distance formula: The formula is D = √[(x2 – x1)2 + (y2 – y1)2 ]. 

Coordinate geometry is used in many fields, including: Trigonometry, Calculus, Dimensional geometry, Statistics, Physics, Construction. 

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Math Practice Test: Coordinate Geometry

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23 Questions

1. In what ratio is the line joining points (3, 8) and (1, 2) divided by the point (7/3, 0)?

2:31:44:11:1

2. The coordinates of the points which divides the line joining A(1, 4) and (6, 4) internally in the ratio 3:4 are

-3, 44, 23, 32, 4

3. Points (1, 1) (4, 4) (4, 8) (0, 4) form _____ type of quadrilateral.

squarecollinear rhombusparallelogram

4. The points (2, 1), (5, 1) and (8, 3)

collinearcoplanar/straight lineform a triangleform a circle

5. The area of the triangle whose vertices are (0, 0), (1, 0) and (0, 1) is

1/2124

6. The point of intersection of the lines 2x + 3y = 7 and
x – 4y = 2 is

(2, -3)(2, 1)(2, 1) (2, 1)

7. What are the intercepts which the line 5x + 3y = 15 makes on the axis ?

5, 33, 51, 15, 1/3

8. Points (1, 1) (4, 4) (4, 8) (0, 4) form _____ type of quadrilateral.

collinear squarerhombusparallelogram

9. Find K if the segment joining A(4, 3) and B(K, 5) is bisected by the line 2x + 3y – 6 = 0

101551

10. The distance between the lines y = 2x + 4 and y = 2x + 8 is

520.40.8

11. The point of intersection of the lines 2x + 3y = 7 and
x – 4y = 2 is

(2, -3)(2, 1)(2, 1)(2, 1)

12. The points (7, 9) (3, –7) (3, 3) are vertices of a _____ triangle.

a and cright angledequilateralisosceles

13. P is a point in the line segment AB such that AP:PB = 3:2. If A is (1, 2) and B(4, 5), the coordinates of P are

13/5, 7/514/5, 9/514/5, 19/513/2, 1/2

14. P is a point in the line segment AB such that AP:PB = 3:2. If A is (1, 2) and B(4, 5), the coordinates of P are

13/5, 7/514/5, 19/513/2, 1/214/5, 9/5

15. The coordinates of two points A and B are (3, 2) and (4, 6). The point P on the line AB divides externally in such a way that AP:AB :: 2:5. Coordinates of P are

2, 3/55, 63/5, 6/529/5, 26/5

16. The area of triangle formed by the points (10,0), (10, 0) and (0, 10) is

1004002050

17. In an equilateral triangle PQR with P(4, 0) and Q(4, 0), R is

none0,4

18. The equation of line Perpendicular to x + 2y = 6 and passing through the intersection of 2x + 3y = 13 and
x + y = 5 is

x – 2y = 12 x + y = 52x y = 12x + y + 1 = 0

19. The equation of locus of a point which is always equidistant from the points (6, 8) and (4, 6) is_____

3x + 2y = 4 x + y = - 2x + y = 124x + 3y = 12

20. In what ratio is the line joining points (3, 8) and (1, 2) divided by the point (7/3, 0)?

2:31:44:11:1

21. Find K if the segment joining A(4, 3) and B(K, 5) is bisected by the line 2x + 3y – 6 = 0

151051

22. The distance between the lines y = 2x + 4 and y = 2x + 8 is

0.40.852

23. What are the intercepts which the line 5x + 3y = 15 makes on the axis ?

5, 33, 51, 15, 1/3