mid-point and distance

Front

What is the formula for finding the midpoint between 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 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

If M(1, -2) is the midpoint of segment GH and G has coordinates (3, 4), how do you find the coordinates of H?

Back

Use the midpoint formula: H = (2M - G). Substitute M and G to find H.

Tags

CCSS.HSG.GPE.B.6

Front

What is the distance between the points (-11, 4) and (4, 4)?

Back

The distance is 15, calculated as d = √((4 - (-11))² + (4 - 4)²) = √(15²) = 15.

Tags

CCSS.HSG.GPE.B.7

Front

What are the coordinates of the midpoint between the points (4, 3) and (0, 6)?

Back

The midpoint is (2, 4.5), calculated as M = ((4 + 0)/2, (3 + 6)/2).

Tags

CCSS.HSG.GPE.B.6

Front

How do you find the coordinates of an endpoint if you know one endpoint and the midpoint?

Back

Use the formula: Endpoint = 2(Midpoint) - Known Endpoint.

Tags

CCSS.HSG.GPE.B.6

Front

What is the distance between the points (4, 3) and (0, 6)?

Back

The distance is 5, calculated as d = √((0 - 4)² + (6 - 3)²) = √(16 + 9) = √25 = 5.

Tags

CCSS.HSG.GPE.B.7

Front

If the midpoint is (-8, -5) and one endpoint is (-6, -3), what is the other endpoint?

Back

The other endpoint is (-10, -7), calculated using the formula: Endpoint = 2(Midpoint) - Known Endpoint.

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 the distance formula be derived from the Pythagorean theorem?

Back

The distance formula is derived by considering the difference in x and y coordinates as the legs of a right triangle, applying the Pythagorean theorem.

Tags

CCSS.HSG.GPE.B.7