Exploring the Midpoint Formula

This video tutorial covers the midpoint formula in geometry, explaining how to find the midpoint of a line segment. It starts with the definition of a midpoint and methods for finding midpoints of vertical or horizontal lines. The tutorial then introduces the midpoint formula for diagonal lines, providing an example calculation. It also discusses how to work backwards to find endpoints when the midpoint and one endpoint are known, and how to handle cases with unknown or variable coordinates.

What is the term for the point that divides a line segment into two equal parts?

• Midpoint

• Centroid

• Endpoint

• Vertex

How do you find the midpoint of a vertical or horizontal line segment?

• By using the Pythagorean theorem

• By using the distance formula

• By counting the length and dividing by two

• By finding the slope

What is the formula to find the midpoint of 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 a segment with endpoints at (-3, 4) and (2, 1)?

• (-0.5, 2.5)

• (-1, 3)

• (0, 2)

• (-1, 2.5)

What is the average of the x-coordinates for the endpoints (-3, 4) and (2, 1)?

• -0.5

• -1

• 0

• 1

If the midpoint of a segment is (-1, 1) and one endpoint is (1, -3), what is the other endpoint?

• (1, 1)

• (-1, -1)

• (3, -5)

• (-3, 5)

If you know the midpoint and one endpoint of a segment, what method can you use to find the other endpoint?

• Slope formula

• Midpoint formula

• Pythagorean theorem

• Distance formula

When given coordinates as variables, what might your midpoint answer include?

• None of the above

• Variables

• Only fractions

• Only integers

In the example with variable coordinates, what is the midpoint of the segment with endpoints (a, 6) and (a+2, 10)?

• (a, 8)

• (a+1, 8)

• (a+1, 7)

• (a+2, 8)

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

• (k/2, -m/2)

• (-k, m)

• (-k/2, m/2)

• (k, -m)