Midpoint

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 find the midpoint of a line segment with endpoints (-7, -8) and (4, 7)?

Back

The midpoint is M = ((-7 + 4)/2, (-8 + 7)/2) = (-1.5, -0.5).

Tags

CCSS.HSG.GPE.B.6

Front

What is the midpoint of the points (-5, 3) and (4, -5)?

Back

The midpoint is M = ((-5 + 4)/2, (3 - 5)/2) = (-0.5, -1).

Tags

CCSS.HSG.GPE.B.6

Front

What is the distance between the points (-3, -4) and (5, 5)?

Back

The distance is calculated using the distance formula: d = √((x2 - x1)² + (y2 - y1)²) = √((5 - (-3))² + (5 - (-4))²) = 12.

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 and is often used in various geometric constructions.

Tags

CCSS.HSG.GPE.B.6

Front

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

Back

You can verify by checking if the distances from the midpoint to each endpoint are equal.

Tags

CCSS.HSG.GPE.B.6

Front

What is the geometric interpretation of the midpoint of a line segment?

Back

The midpoint is the point that is equidistant from both endpoints of the segment.

Tags

CCSS.HSG.GPE.B.6

Front

If the endpoints of a segment are (2, 3) and (8, 7), what is the midpoint?

Back

The midpoint is M = ((2 + 8)/2, (3 + 7)/2) = (5, 5).

Tags

CCSS.HSG.GPE.B.6

Front

What is the formula to find the distance between two points in a coordinate plane?

Back

The distance formula is d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

How do you find the coordinates of the midpoint of a diagonal in a rectangle?

Back

The midpoint of a diagonal can be found using the midpoint formula applied to the coordinates of the opposite corners.

Tags

CCSS.HSG.GPE.B.6