Coordinate Geometry Practice Questions

Coordinate geometry is a topic from which you could expect from one to two questions in the quant section of the GMAT, GRE, SAT, CAT and the TANCET exams. Concepts tested in this aptitude topic include finding length of a line segment, finding slope of a line, framing equation of a line, finding the quadrants through which a line passes, intercepts of a line with the x and y axes, equation of a circle, area of a triangle, and coordinates of mid point of line segment.

1. Two diagonals of a parallelogram intersect each other at coordinates (17.5, 23.5). Two adjacent points of the parallelogram are (5.5, 7.5) and (13.5, 16). Find the lengths of the diagonals.

   1. 15 and 30
   2. 15 and 40
   3. 17 and 30
   4. 17 and 40
   5. Multiple solution are possible

   Choice DThe lengths of the diagonals are 17 and 40. Correct answer Explanatory Answer Video Explanation XAT 2015

2. The equations of four lines are given: x + 2y - 3 = 0, 3x + 4y - 7 = 0, 2x + 3y - 4 = 0 and 4x + 5y - 6 = 0. What can be said about the four lines?

   1. Concurrent
   2. Form sides of a parallelogram
   3. Form sides of a square
   4. None of these

   Choice (4)None of these. Correct answer Explanatory Answer Medium

3. Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4). What is the shape of the quadrilateral?

   1. Square
   2. Rectangle but not a square
   3. Rhombus
   4. Parallelogram but not a rhombus

   Choice (3)The quadrilateral is a rhombus. Correct answer Explanatory Answer Easy

4. A and B are two points with the co-ordinates (-2, 0) and (0, 5). What is the length of the diagonal AC if AB form one of the sides of the square ABCD?

   1. \\sqrt{29}\\)
   2. \\sqrt{58}\\)
   3. \\sqrt{116}\\)
   4. \2\sqrt{29}\\)

   Choice (2)The diagonal measures √58. Correct answer Explanatory Answer Easy

5. Find the area of the triangle whose vertices are (-6, -2), (-4, -6), (-2, 5).

   1. 36 sq units
   2. 18 sq units
   3. 15 sq units
   4. 30 sq units

   Choice (3)The area of the triangle is 15 sq units. Correct answer Explanatory Answer Easy

6. Find the equation of a line whose intercepts are twice of the line 3x – 2y – 12 = 0.

   1. 3x – 2y = 24
   2. 2x – 3y = 12
   3. 2x – 3y = 24
   4. None of these

   Choice (1)The equation of the second line is 3x – 2y = 24. Correct answer Explanatory Answer Easy

7. Find the coordinates of the point which divides the line joining (5, -2) and (9, 6) internally in the ratio 1 : 3.

   1. (6, 0)
   2. (6, 3)
   3. (0, 6)
   4. (3, 6)

   Choice (1)The coordinates of the point are (6, 0). Correct answer Explanatory Answer Easy