Distance, Midpoint, Slope, Partition

Front

What is the formula to find 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

What is the definition of the midpoint in geometry?

Back

The midpoint is the point that divides a line segment into two equal parts.

Front

If point A is at (x1, y1) and point B is at (x2, y2), how do you find the coordinates of point B if you know the midpoint and point A?

Back

Use the formula B = (2 * midpoint_x - x1, 2 * midpoint_y - y1).

Front

What is the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated as m = (y2 - y1) / (x2 - x1).

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical.

Front

How do you find the coordinates of a point that divides a line segment in a given ratio?

Back

Use the formula P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where P is the dividing point and m:n is the ratio.

Front

What is the distance between the points (3, 4) and (3, 8)?

Back

The distance is 4, calculated as d = |y2 - y1| = |8 - 4|.

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.