Distance, Midpoint, Endpoint

Front

What is the formula to 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 is the definition of the midpoint of a line segment?

Back

The midpoint of a line segment is the point that divides the segment into two equal parts. It can be calculated using the formula: Midpoint = ((x1 + x2)/2, (y1 + y2)/2).

Tags

CCSS.HSG.GPE.B.6

Front

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

Back

If you have one endpoint (x1, y1) and the midpoint (xm, ym), the other endpoint (x2, y2) can be found using the formulas: x2 = 2*xm - x1 and y2 = 2*ym - y1.

Tags

CCSS.HSG.GPE.B.6

Front

What is the distance between the points (1, 2) and (4, 6)?

Back

The distance is calculated as d = √((4 - 1)² + (6 - 2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Tags

CCSS.HSG.GPE.B.7

Front

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

Back

The midpoint is calculated as Midpoint = ((2 + 8)/2, (3 + 7)/2) = (5, 5).

Tags

CCSS.HSG.GPE.B.6

Front

What is the distance between the points (-3, -4) and (1, 2)?

Back

The distance is d = √((1 - (-3))² + (2 - (-4))²) = √((1 + 3)² + (2 + 4)²) = √(4² + 6²) = √(16 + 36) = √52.

Tags

CCSS.HSG.GPE.B.7

Front

How do you calculate the distance between two points in a coordinate plane?

Back

To calculate the distance, use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

What is the formula for finding the other endpoint when given one endpoint and the midpoint?

Back

The formulas are: x2 = 2*xm - x1 and y2 = 2*ym - y1, where (xm, ym) is the midpoint.

Tags

CCSS.HSG.GPE.B.6

Front

If the midpoint of a segment is (3, 4) and one endpoint is (1, 2), what is the other endpoint?

Back

Using the formulas, the other endpoint is (2*3 - 1, 2*4 - 2) = (5, 6).

Tags

CCSS.HSG.GPE.B.6

Front

What is the distance between the points (0, 0) and (3, 4)?

Back

The distance is d = √((3 - 0)² + (4 - 0)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.

Tags

CCSS.HSG.GPE.B.7