Exploring the Triangle Inequality Theorem and Distance on the Coordinate Plane

The video tutorial covers two main topics: the triangle inequality theorem and calculating distance on a coordinate plane. It begins with a review of bell ringer exercises, followed by an explanation of the triangle inequality theorem, including examples to determine if given side lengths form a triangle. The lesson then transitions to finding distances on a coordinate plane using the Pythagorean theorem and the distance formula, with practical examples and exercises.

What is the least common multiple (LCM) used to eliminate fractions in the bell ringer exercises?

• 6

• 2

• 3

• 9

According to the triangle inequality theorem, what must be true for three side lengths to form a triangle?

• The difference between any two side lengths must be less than the third side length.

• The product of any two side lengths must be greater than the third side length.

• The sum of all three side lengths must be equal.

• The sum of any two side lengths must be greater than the third side length.

In the example given, do the side lengths 15, 16, and 30 form a triangle?

• Yes

• No

• Only if they are right triangle sides

• Only if they are isosceles triangle sides

Which of the following sets of side lengths does NOT form a triangle?

• 7, 10, 12

• 5, 5, 5

• 3, 4, 5

• 2, 2, 5

What is the range of possible distances from Marcus's house to the Sportplex if he takes the direct route?

• Greater than 2.5 miles but less than 8.5 miles

• Greater than 4.5 miles but less than 6.3 miles

• Greater than 3.5 miles but less than 7.3 miles

• Greater than 1.7 miles but less than 9.3 miles

What formula is used to find the distance between two points on a coordinate plane?

• D = √((x2 - x1)^2 + (y2 - y1)^2)

• D = (x2 - x1) + (y2 - y1)

• D = (x2 - x1)^2 + (y2 - y1)^2

• D = √((x2 + x1)^2 + (y2 + y1)^2)

What is the distance between the points (7, -5) and (3, 0) rounded to the nearest tenth?

• 7.2

• 6.4

• 5.0

• 8.1

If each unit on the map represents 0.5 miles, how many miles longer is Trail B than Trail A?

• 1.5 miles

• 1 mile

• 0.5 miles

• 2 miles

What is the distance between the points (6, 6) and (-3, 1) on Trail A?

• 6.5 miles

• 5.4 miles

• 7.2 miles

• 8.3 miles

What is the distance between the points (6, 6) and (-3, 1) on Trail B?

• 7.2 miles

• 8.3 miles

• 5.4 miles

• 6.5 miles