Coordinate Geometry: Solving Questions Using the Distance Formula

The video tutorial discusses the approach to solving geometry problems, focusing on collinearity of points, types of triangles, and determining if points form a square. It explains using the distance formula to check collinearity and identify triangle types, including right angle triangles using Pythagoras' theorem. The tutorial also covers verifying if points form a square by checking side lengths and diagonals. An exercise is provided for practice.

What is the condition for three points to be collinear?

• The distances between all pairs of points are equal.

• The sum of the distances between two pairs of points is less than the third pair.

• The sum of the distances between two pairs of points is greater than the third pair.

• The sum of the distances between two pairs of points equals the distance of the third pair.

How can you identify a scalene triangle?

• Only two sides are of equal length.

• All sides are of equal length.

• It has a right angle.

• All sides are of different lengths.

Which type of triangle has all sides of different lengths?

• Scalene triangle

• Right-angled triangle

• Isosceles triangle

• Equilateral triangle

Which theorem is used to verify if a triangle is right-angled?

• Pythagorean theorem

• Triangle inequality theorem

• Sine rule

• Cosine rule

What additional property must be checked to confirm a quadrilateral is a square?

• All angles are right angles.

• Diagonals are equal.

• All sides are parallel.

• Opposite sides are equal.

If a quadrilateral has equal diagonals, what shapes could it potentially be?

• Only a square

• Only a rectangle

• A square, rectangle, or isosceles trapezium

• Only a rhombus

What is the primary formula used to determine distances between points in coordinate geometry?

• Distance formula

• Slope formula

• Midpoint formula

• Area formula