NSEJS - coordinate geometry

Coordinate Geometry - Singapore Maths Olympiad

Let A and B be points that lie on the parabola y = x² such that both are at a distance of 8√2 units from the line y = -x – 4. Find the square of distance between A and B

coordinate geometry

Show that the lines x = 0 and y = 0 trisect the line segment formed by joining the points (-10, -4) and (5,8). Find the point of trisection.

Coordinate Geometry

Compute the area of the triangle with vertices at the coordinates (1337, 1337), (1337, 1344), and (1349, 1337)

 Gator Mathematics Competition 2013

23-coordinate geometry

If the points A (1, –2), B (2, 3) C (a, 2) and D (– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as base.

22-coordinate geometry

If (-4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.

21-coordinate geometry

The mid-points D, E, F of the sides of a triangle ABC are (3, 4), 

(8, 9) and (6, 7). Find the coordinates of the vertices of the triangle.

                        

20-coordinate geometry

Find the ratio in which the line 2x + 3y – 5 = 0 divides the line segment joining the points (8, –9) and (2, 1). Also find the coordinates of the point of division.

19-coordinate geometry

Find the values of k if the points A (k + 1, 2k), B (3k, 2k + 3) and 

C (5k – 1, 5k) are collinear.

18 coordinate geometry

If (a, b) is the mid-point of the line segment joining the points 

A (10, –6) and B (k, 4) and a – 2b = 18, find the value of k and the distance AB.

17coordinate geometry

If the points A (1, 2), O (0, 0) and C (a, b) are collinear, then

(A) a = b          (B) a = 2b       (C) 2a = b       (D) a = –b

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16 Coordinate Geometry

 The area of a triangle with vertices (a, b + c), (b, c + a) and 

(c, a + b) is

(A) (a + b + c)²     (B) 0                (C) a + b + c               (D) abc

15-coordinate Geometry

A line intersects the y-axis and x-axis at the points P and Q, respectively.If (2, –5) is the mid-point of PQ, then the coordinates of P and Q are, respectively

(A) (0, – 5) and (2, 0)                          (B) (0, 10) and (– 4, 0)          

                                                           

(C) (0, 4) and (– 10, 0)                        (D) (0, – 10) and (4, 0)

14-coordinate geometry

The perpendicular bisector of the line segment joining the points A (1, 5) and B (4, 6) cuts the y-axis at

(A) (0, 13)        (B) (0, –13)     (C) (0, 12)        (D) (13, 0)

13-Coordinate Geometry

If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8, 4), then 

 

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12-coordinate geometry

The fourth vertex D of a parallelogram ABCD whose three vertices are A (–2, 3), B (6, 7) and C (8, 3) is

(A) (0, 1)          (B) (0, –1)       (C) (–1, 0)       (D) (1, 0)

11-coordinate geometry

The point which lies on the perpendicular bisector of the line segment joining the points A (–2, –5) and B (2, 5) is

(A) (0, 0)          (B) (0, 2)         (C) (2, 0)         (D) (–2, 0)

10 coordinate geometry

The equation of a line is 2y – 3x = 5. A mirror is placed at x = 6.

Find the equation of line of the mirror image.

9 - equation of line parallel to given line

Two points A and B have the following coordinated (2, 2) and 

(10, 8) respectively.

Find the equation of straight line which passes through point (3, 4) and is Parallel to AB?

8-equation of perpendicular to given line

Two points A and B have the following coordinated (2, 2) and 

(10, 8) respectively.

Find the equation of straight line which passes through point (3, 4) and in perpendicular to AB?