Midpoint and Distance Review

Front

What is the distance formula used to find the distance between two points (x1, y1) and (x2, y2)?

Back

The distance formula is given by: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Tags

CCSS.HSG.GPE.B.7

Front

How do you calculate the midpoint of a line segment with endpoints A (x1, y1) and B (x2, y2)?

Back

The midpoint M is calculated using the formula: \( M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \)

Tags

CCSS.HSG.GPE.B.6

Front

What is the distance between the points (-4, 5) and (7, 18)?

Back

The distance is approximately 17.03.

Tags

CCSS.HSG.GPE.B.7

Front

What is the midpoint of the points A (6, -4) and B (-4, 8)?

Back

The midpoint is \( (1, 2) \).

Tags

CCSS.HSG.GPE.B.6

Front

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

Back

If C is the known endpoint and M is the midpoint, the other endpoint D can be found using: \( D = (2M_x - C_x, 2M_y - C_y) \)

Tags

CCSS.HSG.GPE.B.6

Front

What is the distance between the points (-12, 1) and (12, -1)?

Back

The distance is approximately 24.08.

Tags

CCSS.HSG.GPE.B.7

Front

What is the midpoint of the segment with endpoints (4, 12) and (-6, 14)?

Back

The midpoint is (-1, 13).

Tags

CCSS.HSG.GPE.B.6

Front

If the midpoint M is (5, -3) and one endpoint C is (2, -4), what is the other endpoint?

Back

The other endpoint is \( (8, -2) \).

Tags

CCSS.HSG.GPE.B.6

Front

What is the significance of the distance formula in geometry?

Back

The distance formula is used to determine the length of a line segment between two points in a coordinate plane.

Tags

CCSS.HSG.GPE.B.7

Front

What are the coordinates of the midpoint of a segment with endpoints (x1, y1) and (x2, y2)?

Back

The coordinates of the midpoint are \( \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \).

Tags

CCSS.HSG.GPE.B.6