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).

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).

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.

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.

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).

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.

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.

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.

Front

What is the significance of the midpoint in geometry?

Back

The midpoint divides a line segment into two equal parts.

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.