What is the formula to calculate the distance between two points (x₁, y₁) and (x₂, y₂)?

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

True or False: The distance formula is applicable only in the first quadrant of the Cartesian plane.

False. The distance formula works in any quadrant, but correct signs for coordinates must be used.

Fill in the blank: The circumcentre is the point ______ from all three vertices of a triangle.

Equidistant

Which of the following points lies on the y-axis? A) (3, 0) B) (0, 5) C) (4, 6) D) (2, -3)

B) (0, 5)

Riddle: I am the point that is the center of a circle passing through all vertices of a triangle. What am I?

Circumcentre

To find the circumcentre of triangle ABC, one must set PA equal to PB and ______.

PA equal to PC

True or False: Points are collinear if the distances AB + BC = AC.

True

What is the distance from the origin (0, 0) to the point (x, y)?

Distance = √(x² + y²)

Fill in the blank: A ______ has all sides equal and diagonals equal.

Square

Which of the following statements is true regarding a parallelogram? A) All angles are 90 degrees B) Opposite sides are equal C) All sides are equal D) Diagonals bisect at right angles

B) Opposite sides are equal

Short Answer: What does it mean for points to be collinear?

Points are collinear if the sum of the distances between any two pairs equals the distance of the third pair.

Riddle: I am a formula that finds the distance between two points, and I involve squares and a root. What am I?

Distance Formula

True or False: The circumradius is the distance from the circumcentre to any vertex of the triangle.

True

Fill in the blank: The coordinates of a point dividing a line segment in a specific ratio can be found using ______.

Section formula

Which of the following is NOT a property of a rhombus? A) All sides are equal B) Opposite angles are equal C) Diagonals bisect each other at right angles D) All sides are unequal

D) All sides are unequal

What is the significance of the distance formula in coordinate geometry?

It measures the straight-line distance between two points on a coordinate plane.

Fill in the blank: The midpoint of a line segment can be found by averaging the ______ of the endpoints.

Coordinates

True or False: The distance between two points can be negative.

False. Distance is always a non-negative value.

Which equation represents the relationship between the sides of an isosceles right-angled triangle? A) AB² + AC² = BC² B) AB + AC = BC C) AB² = AC² D) AB + BC = AC

A) AB² + AC² = BC²

What is the formula to calculate the distance between two points (x₁, y₁) and (x₂, y₂) on a Cartesian plane?

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]