Distance, Midpoint, & Endpoint

Front

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

Back

The midpoint M is given by M = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right).

Tags

CCSS.HSG.GPE.B.6

Front

How do you find the other endpoint of a line segment when given one endpoint and the midpoint?

Back

Use the formula: Endpoint = 2 * Midpoint - Given Endpoint.

Tags

CCSS.HSG.GPE.B.6

Front

What is the distance formula between two points (x1, y1) and (x2, y2)?

Back

The distance D is given by D = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}.

Tags

CCSS.HSG.GPE.B.7

Front

If the midpoint of a segment is (0, 9) and one endpoint is (9, 8), what is the other endpoint?

Back

The other endpoint is (-9, 10).

Tags

CCSS.HSG.GPE.B.6

Front

What is the midpoint of the points (-4, 4) and (-2, 2)?

Back

The midpoint is (-3, 3).

Tags

CCSS.HSG.GPE.B.6

Front

Given the endpoints (-4, 5) and (7, -9), find the other endpoint if one is known.

Back

The other endpoint is (18, -23).

Tags

CCSS.HSG.GPE.B.6

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 distances from the midpoint to both endpoints are equal.

Tags

CCSS.HSG.GPE.B.6

Front

What is the geometric interpretation of the distance formula?

Back

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

Tags

CCSS.HSG.GPE.B.7

Front

If the coordinates of a midpoint are (3, -1), what could be one possible pair of endpoints?

Back

One possible pair of endpoints could be (1, -3) and (5, 1).

Tags

CCSS.HSG.GPE.B.6