Exploring the Midpoint Formula in Geometry

This video tutorial by Mr. Backberg introduces the concept of the midpoint in geometry, explaining how it divides a segment into two congruent parts. The tutorial covers the use of algebraic expressions to find segment lengths and demonstrates the midpoint formula for determining the midpoint of a segment on a coordinate plane. It also includes examples of finding a missing endpoint using the midpoint formula.

What does the midpoint of a segment do?

• Changes the length of the segment

• Divides the segment into two unequal parts

• Divides the segment into two congruent segments

• Marks the end of the segment

How do we visually show that two segments are congruent?

• By coloring them differently

• By labeling them with different letters

• By putting a slash mark on them

• By drawing a circle around them

If VM = 4x - 1 and MW = 3x + 3, what is the value of x?

• 5

• 4

• 3

• 2

What is the midpoint formula for a segment with endpoints (x1, y1) and (x2, y2)?

• ((x1 / x2) / 2, (y1 / y2) / 2)

• ((x1 * x2) / 2, (y1 * y2) / 2)

• ((x1 - x2) / 2, (y1 - y2) / 2)

• ((x1 + x2) / 2, (y1 + y2) / 2)

What is the midpoint of the segment with endpoints (-1, -2) and (3, -4)?

• (1, -3)

• (0, -3)

• (1, -2)

• (2, -3)

What is the midpoint of the segment with endpoints (-3, 1) and (7, -5)?

• (1, -2)

• (1, -3)

• (2, -3)

• (2, -2)

What is the midpoint of the segment with endpoints (4, 3) and (2, -3)?

• (2, -1)

• (3, -1)

• (2, 0)

• (3, 0)

Given one endpoint (-5, 0) and the midpoint (-2, 7), what is the other endpoint?

• (1, 13)

• (0, 14)

• (1, 14)

• (0, 13)

If the midpoint of a segment is (3, 0) and one endpoint is (4, 3), what is the other endpoint?

• (2, -2)

• (1, -3)

• (2, -3)

• (1, -2)

What is the first step in finding the other endpoint given one endpoint and the midpoint?

• Multiply the coordinates of the midpoint

• Subtract the coordinates of the midpoint

• Divide the coordinates of the midpoint

• Add the coordinates of the midpoint