Triangle Properties and Calculations

The video tutorial demonstrates how to use the distance formula to calculate the lengths of the sides of triangle ABC, verify it as a right triangle using the Pythagorean theorem, and finally calculate its area. The coordinates of the vertices are given, and the process involves step-by-step calculations to ensure accuracy. The tutorial emphasizes understanding the geometric principles and applying them to solve the problem effectively.

What is the main objective of the problem discussed in the video?

• To calculate the volume of a 3D shape

• To verify if triangle ABC is a right triangle

• To determine the type of triangle based on angles

• To find the perimeter of triangle ABC

What are the coordinates of vertex A of triangle ABC?

• (-3, 10)

• (4, 7)

• (1, 0)

• (0, 0)

Which formula is used to calculate the length of side AB?

• Area formula

• Distance formula

• Volume formula

• Slope formula

What is the length of side AB?

• Square root of 49

• Square root of 58

• Square root of 116

• Square root of 9

What is the alternate method used to calculate the length of side BC?

• Using the midpoint formula

• Using the change in x and y values

• Using the area formula

• Using the slope formula

What is the length of side BC?

• Square root of 49

• Square root of 58

• Square root of 116

• Square root of 9

How many places does the x-coordinate move from B to C?

• 3 places

• 4 places

• 7 places

• 10 places

What is the length of side AC?

• Square root of 9

• Square root of 58

• Square root of 49

• Square root of 116

What is the total distance moved from vertex A to C?

• 14 places

• 16 places

• 10 places

• 4 places

Which theorem is used to verify that triangle ABC is a right triangle?

• Cosine rule

• Triangle inequality theorem

• Pythagorean theorem

• Sine rule