Coordinate Geometry

Which of the following points is on line k, given the line has a slope of -1/3 and passes through the point (5, 8)?

1. (7, 9)
2. (5, 8)
3. (1, 4)
4. (2, 9)

Answer: (d) (2, 9)

Find the coordinates of the points on the x-axis that are at a distance of 10 units from the point (-4, 8).

1. (2, 0), (5, 0)
2. (5, 0), (-3, 0)
3. (-10, 0), (2, 0)
4. (2, 0), (1,0)

Answer: (c) (-10, 0), (2, 0)

PQR is a triangle and the vertices of the triangle are (1, -1), (-1/2, 1/2) and (1, 2). These coordinates are of which triangle?

1. Scalene triangle
2. Isosceles triangle
3. Equilateral triangle
4. Right-angled triangle

Answer: (b) Isosceles triangle

If points A (K, -K) and B (K + 1, K) are on a circle with the centre at the origin, find the difference between the maximum and minimum possible values of K.

1. 2
2. 4
3. 0
4. -1/2

Answer: (c) 0

In what ratio is the line joining the points A(4, 4) and B(7, 7) divided by P(-1, 1)?

1. 6 : 7
2. 5 : 8
3. 8 : 9
4. 1 : 3

Answer: (b) 5 : 8

The medians AD and BE of the triangle with vertices A(0, b) and C(a, 0) are mutually perpendicular. Which of the options is correct according to the above statement?

1. a = ±√(2)b
2. b = -√(2)a
3. b = √(2)a
4. a = b

Answer: (a) a = ±√(2)b

What is the slope of a line perpendicular to the line which passes through the points (-k, h) and (b, -f)?

1. (b + k)/(f + h)
2. (b - k)/(f + h)
3. (h + k)/(b - f)
4. (b - f)/(h + k)

Answer: (a) (b + k)/(f + h)

Find the ratio in which the line joining points (a + b, b + a) and (a - b, b - a) is divided by the point (a, b).

1. 2 : 1 externally
2. a : b externally
3. 1 : 1 internally
4. b : a internally

Answer: (c) 1 : 1 internally

What is the angle between the lines 3x + y - 7 = 0 and x + 2y + 9 = 0?

1. 45o
2. 90o
3. 15o
4. 60o

Answer: (a) 45o

Find the equation of a line passing through the point of intersection of the lines 5x − y − 7 = 0 and 3x − 2y − 7 = 0 and parallel to the x + 3y − 5 = 0.

1. x + 3y - 5 = 0
2. 2x - 3y + 5 = 0
3. x - 6y + 5 = 0
4. x + 3y + 5 = 0

Answer: (d) x + 3y + 5 = 0