The point that divides the line segment joining (-2, 3) and (1, -1) in the ratio 2:1 internally is:

a) (0, 1/3)

b) (1/2, -1/2)

c) (1/2, 1/2)

d) (-1/2, -1/2)

The points (2, 3) and (5, 1) are endpoints of a line segment. Find the midpoint of this line segment.

a) (3.5, 2.5)

b) (3, 2)

c) (2, 3)

d) (3.5, 2)

The point (3, a) lies on the line with the equation \(2x – 3y = 8\). What is the value of a for this point?

a) -2

b) 2

c) 3

d) \(-\frac{2}{3}\)

The equation of the line parallel to the y-axis and passing through the point (2, -5) is:

a) y = 2

b) x = 2

c) y = -5

d) x = -5

The section formula for the point that divides the line joining (2, -3) and (-4, 5) in the ratio 3:2 internally is:

a) (0, 1)

b) \((-\frac{5}{2}, 3)\)

c) (1, 0)

d) (0, -1)

The points (4, 6) and (8, 12) are endpoints of a line segment. Find the midpoint of this line segment.

a) (6, 9)

b) (5, 8)

c) (4, 6)

d) (8, 12)

Which of the following statements is true about the diagonals of a rectangle?

a) The diagonals are not perpendicular to each other.

b) The diagonals are equal in length.

c) The diagonals bisect each other.

d) All of the above.

Which of the following statements is true about the diagonals of a square?

a) The diagonals are perpendicular to each other.

b) The diagonals are equal in length.

c) The diagonals bisect each other.

d) All of the above.

The point that divides the line segment joining (-1, 2) and (3, -4) in the ratio 2:3 internally is:

a) (2, -3)

b) (-2, 3)

c) \((\frac{2}{5}, -\frac{2}{5})\)

d) (-1, 1)

The distance between the points (1, 2) and (1, 5) is:

a) 3

b) 5

c) 4

d) 7