Coordinate Geometry Quiz

Find the inclination of the line passing through the points (3, 7) and (9, 1).

1. 90o
2. 45o
3. 135o
4. 30o

Answer: (c) 135o

Find the acute angle, which is the perpendicular from the origin on the line 3x + 3y = 4 makes with the x - axis.

1. 90o
2. 30o
3. 135o
4. 45o

Answer: (d) 45o

The equation of one of the diagonals of a rhombus is 5x - 2y + 3 = 0. Find the equation of the other diagonal passing through the point (2, -1).

1. 3x + 6y = - 1
2. 2x + 10y = 1
3. 2x + 5y = 1
4. 2x + 5y = - 1

Answer: (d) 2x + 5y = - 1

Find the point of trisection of the line segment joining the points (2, 3) and (14, 12).

1. (6, 6), (10, 9)
2. (6, 5), (11, 9)
3. (5, 6), (9, 11)
4. (6, 6), (9, 10)

Answer: (a) (6, 6), (10, 9)

The line through the points (4, 3) and (2, 5) cuts off the intercepts of lengths λ and μ on the axis. What is the value of λ and μ?

1. (1, 8)
2. (2, 3)
3. (1, 7)
4. (7, 7)

Answer: (d) (7, 7)

(0,0), (3, √3) and (0,2√3) are the three vertices of a triangle. Find the distance between the orthocentre and the circumcentre of the triangle.

1. √13
2. √10
3. 0
4. 1

Answer: (c) 0

What is the product of the perpendicular distance from the two points ((±√b2 - a2), 0) to the line ax + by = ab?

1. a4/(a2 + b2)
2. -a4/(a2 + b2)
3. -a2/(a4 + b4)
4. a4/(a4 + b4)

Answer: (b) -a4/(a2 + b2)

The line segment joining P(5, -2) and Q(9, 6) is divided into the ratio 3 : 1 by a point on A on it. Find the equation of a line through the point A parallel to line x - 3y + 4 = 0

1. 3y - x = 4
2. 3y - 3x = 16
3. 3x - y = 4
4. 3y - x = 12

Answer: (a) 3y - x = 4

Read the following passage and answer the following question: The line y = 2x - 3 meets the x-axis at the point P, and the line 3y + 4x = 8 meets the x-axis at the point Q. The two lines intersect at the point R. Find the coordinates of R.

1. (17, 5)
2. (1.7, 0.4)
3. (14, 8)
4. (19, 5)

Answer: (b) (1.7, 0.4)

Read the following passage and answer the following question: The line y = 2x - 3 meets the x-axis at the point P, and the line 3y + 4x = 8 meets the x-axis at the point Q. The two lines intersect at the point R. Find the area of triangle PQR.

1. 1
2. 0.3
3. 0.1
4. 0

Answer: (c) 0.1