Midpoint Formula

Front

What is the Midpoint Formula?

Back

The Midpoint Formula is used to find the midpoint (M) of a line segment with endpoints (x1, y1) and (x2, y2). It is given by: M = ((x1 + x2)/2, (y1 + y2)/2).

Tags

CCSS.HSG.GPE.B.6

Front

Find the midpoint of the line segment with endpoints (-3, -5) and (7, 8).

Back

M = ((-3 + 7)/2, (-5 + 8)/2) = (2, 1.5).

Tags

CCSS.HSG.GPE.B.6

Front

How do you find the other endpoint of a line segment if you know one endpoint and the midpoint?

Back

If A(x1, y1) is one endpoint and M(xm, ym) is the midpoint, the other endpoint B(x2, y2) can be found using: x2 = 2*xm - x1 and y2 = 2*ym - y1.

Tags

CCSS.HSG.GPE.B.6

Front

Given endpoint A(6, -9) and midpoint M(-2, 10), find the other endpoint B.

Back

Using the formula: B = (2*-2 - 6, 2*10 - (-9)) = (-10, 29).

Tags

CCSS.HSG.GPE.B.6

Front

What is the significance of the Midpoint Formula in geometry?

Back

The Midpoint Formula helps in determining the center point of a line segment, which is crucial for various geometric constructions and proofs.

Tags

CCSS.HSG.GPE.B.6

Front

Find the midpoint of the line segment with endpoints (-1, -3) and (3, 5).

Back

M = ((-1 + 3)/2, (-3 + 5)/2) = (1, 1).

Tags

CCSS.HSG.GPE.B.6

Front

If the midpoint of a line segment is (4, 2) and one endpoint is (6, 3), what is the other endpoint?

Back

Using the formula: B = (2*4 - 6, 2*2 - 3) = (2, 1).

Tags

CCSS.HSG.GPE.B.6

Front

What is the formula to calculate the distance between two points?

Back

Tags

CCSS.HSG.GPE.B.7

Front

Find the midpoint of the line segment with endpoints (-2.5, -7) and (-10, -3).

Back

M = ((-2.5 - 10)/2, (-7 - 3)/2) = (-6.25, -5).

Tags

CCSS.HSG.GPE.B.6

Front

What is the relationship between the midpoint and the endpoints of a line segment?

Back

The midpoint is equidistant from both endpoints of the line segment, meaning it divides the segment into two equal parts.

Tags

CCSS.HSG.GPE.B.6