# Coordinate Geometry Practice Questions

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Coordinate geometry is a topic from which you could expect from one to two questions in the XAT and the TANCET exams. Concepts covered 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
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
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
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. $2\sqrt{29}\\$ 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
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
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)