13.3 Rounding, Distance, Midpoint, Endpoint

Front

What is the midpoint formula for two points (x1, y1) and (x2, y2)?

Back

The midpoint M is given by M = ((x1 + x2)/2, (y1 + y2)/2).

Tags

CCSS.HSG.GPE.B.6

Front

How do you calculate the distance between two points (x1, y1) and (x2, y2)?

Back

The distance D is calculated using the formula D = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

What are the coordinates of the midpoint of the segment with endpoints (-7, -8) and (4, 7)?

Back

The midpoint is (-1.5, -0.5).

Tags

CCSS.HSG.GPE.B.6

Front

If G is the midpoint of segment HK, and G is at (-2, 4) with H at (3, 5), how do you find K?

Back

Use the midpoint formula: K = (2G - H). Thus, K = (-7, 3).

Tags

CCSS.HSG.GPE.B.6

Front

Given one endpoint (-4, 5) and midpoint (7, -9), how do you find the other endpoint?

Back

Use the formula: Other endpoint = (2 * midpoint - endpoint). Thus, the other endpoint is (18, -23).

Tags

CCSS.HSG.GPE.B.6

Front

What is the distance between the points (3, 1) and (-2, -1)?

Back

Using the distance formula, the distance is √((-2 - 3)² + (-1 - 1)²) = √(25 + 4) = √29.

Tags

CCSS.HSG.GPE.B.7

Front

What is the significance of the midpoint in geometry?

Back

The midpoint divides a line segment into two equal parts.

Tags

CCSS.HSG.GPE.B.6

Front

How can you verify if a point is the midpoint of a segment?

Back

Check if the coordinates of the point satisfy the midpoint formula for the segment's endpoints.

Tags

CCSS.HSG.GPE.B.6

Front

What is the geometric interpretation of the distance formula?

Back

It represents the length of the straight line connecting two points in a Cartesian plane.

Tags

CCSS.HSG.GPE.B.7

Front

What is the relationship between the coordinates of the midpoint and the endpoints?

Back

The coordinates of the midpoint are the averages of the corresponding coordinates of the endpoints.

Tags

CCSS.HSG.GPE.B.6