Exploring Distance and Midpoint Concepts

The video tutorial covers plotting triangle vertices, labeling sides, and calculating side lengths using the Pythagorean theorem. It explains the derivation of the distance formula from the Pythagorean theorem and introduces the midpoint formula. The tutorial includes practice problems to apply the distance and midpoint formulas, enhancing understanding of these geometric concepts.

What is the first step in plotting the vertices of a triangle?

• Use the Pythagorean theorem.

• Calculate the side lengths.

• Sketch the triangle.

• Label the sides with lowercase letters.

How are the sides of a triangle labeled in relation to their opposite angles?

• With symbols.

• With numbers.

• With lowercase letters.

• With colors.

What is the length of side A if it is between vertices C and B and has 5 units?

• 3 units

• 6 units

• 5 units

• 4 units

Which theorem is used to find the length of side C in a right triangle?

• Triangle inequality theorem

• Sine rule

• Pythagorean theorem

• Cosine rule

What is the distance formula derived from?

• Cosine rule

• Pythagorean theorem

• Sine rule

• Triangle inequality theorem

What is the distance between points (-2, 6) and (3, 7) using the distance formula?

• √25 units

• √61 units

• √36 units

• √26 units

How do you find the midpoint of a line segment?

• By multiplying the coordinates.

• By dividing the coordinates.

• By subtracting the coordinates.

• By finding the average of the x-coordinates and y-coordinates.

What is the midpoint of the segment with endpoints (-2, 6) and (3, 7)?

• (1/2, 6)

• (1, 7)

• (0, 6.5)

• (1/2, 13/2)

What are the coordinates of point F if (1/2, -5/4) is the midpoint of segment FG and G is (4, -7)?

• (-3, 9/2)

• (3, -9/2)

• (-3, -9/2)

• (3, 9/2)

What is the first step in using algebra to find the coordinates of an unknown endpoint given the midpoint and one endpoint?

• Multiply the coordinates.

• Set up equations for the x and y coordinates.

• Subtract the coordinates.

• Divide the coordinates.