Pythagorean Theorem Applications in Triangles

This video tutorial explains how to find the distance between two points in the coordinate plane using the Pythagorean Theorem. It outlines the steps to plot points, draw line segments to form a right triangle, and calculate the hypotenuse. The tutorial includes examples and demonstrates how to find the perimeter of a triangle by creating right triangles and calculating their hypotenuses.

What is the main goal of using the Pythagorean Theorem in the coordinate plane?

• To find the area of a triangle

• To determine the midpoint of a segment

• To calculate the slope of a line

• To find the distance between two points

What is the first step in finding the distance between two points in the coordinate plane?

• Draw a line segment

• Calculate the hypotenuse

• Form a right triangle

• Plot the two points

After plotting the points, what is the next step in the process?

• Form a right triangle

• Find the midpoint

• Draw a line segment connecting the points

• Calculate the hypotenuse

What is the purpose of drawing two additional line segments in the coordinate plane?

• To form a right triangle

• To calculate the area

• To create a square

• To find the midpoint

Which formula is used to calculate the hypotenuse in the coordinate plane?

• a + b = c^2

• a^2 + b^2 = c

• a^2 - b^2 = c^2

• a^2 + b^2 = c^2

In the first example, what are the coordinates of the two points plotted?

• (4, 7) and (-6, -3)

• (1, 6) and (-3, -2)

• (2, 3) and (6, 7)

• (0, 0) and (5, 5)

What is the length of the hypotenuse in the first example after calculation?

• 8.0 units

• 7.5 units

• 8.9 units

• 9.1 units

In the second example, what is the length of each leg of the triangle?

• 5 and 5

• 8 and 8

• 10 and 10

• 12 and 12

What is the calculated hypotenuse in the second example?

• 14.1 units

• 12.1 units

• 15.0 units

• 13.5 units

What is the perimeter of a triangle in the coordinate plane?

• The length of the longest side

• The distance between two points

• The area of the triangle

• The sum of all three sides