Midpoint

Front

What is the definition of a midpoint in geometry?

Back

The midpoint is the point that divides a line segment into two equal parts, located halfway between the endpoints.

Tags

CCSS.HSG.GPE.B.6

Front

How do you find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)?

Back

The midpoint M is calculated using the formula M = ((x1 + x2)/2, (y1 + y2)/2).

Tags

CCSS.HSG.GPE.B.6

Front

Given the midpoint (3, 4) and one endpoint (-1, 6), how do you find the other endpoint?

Back

Use the formula: Other endpoint = (2 * midpoint - given endpoint). For this case, it is (2*3 - (-1), 2*4 - 6) = (7, 2).

Tags

CCSS.HSG.GPE.B.6

Front

What is the formula to find an endpoint when given the midpoint and the other endpoint?

Back

Endpoint = (2 * midpoint - other endpoint).

Tags

CCSS.HSG.GPE.B.6

Front

If the endpoints of a segment are (4, 12) and (-6, 14), what is the midpoint?

Back

The midpoint is calculated as M = ((4 + (-6))/2, (12 + 14)/2) = (-1, 13).

Tags

CCSS.HSG.GPE.B.6

Front

How do you find the missing endpoint if one endpoint is at (-9, -1) and the midpoint is (-2, -6)?

Back

Use the formula: Missing endpoint = (2 * midpoint - known endpoint). Here, it is (2 * (-2) - (-9), 2 * (-6) - (-1)) = (5, -11).

Tags

CCSS.HSG.GPE.B.6

Front

What is the significance of the midpoint in coordinate geometry?

Back

The midpoint helps in determining the center point of a line segment, which is useful in various geometric constructions and proofs.

Tags

CCSS.HSG.GPE.B.6

Front

If the midpoint of a segment is (7, -9) and one endpoint is (-4, 5), how do you find the other endpoint?

Back

Use the formula: Other endpoint = (2 * midpoint - given endpoint). Here, it is (2*7 - (-4), 2*(-9) - 5) = (18, 13).

Tags

CCSS.HSG.GPE.B.6

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

Front

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

Back

Check if the distances from the midpoint to each endpoint are equal.

Tags

CCSS.HSG.GPE.B.6