5. Distance & Line Segments Application

Front

What is a line segment?

Back

A line segment is a part of a line that is bounded by two distinct endpoints.

Front

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

Back

The midpoint M is given by the formula M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the distance formula between two points A(x1, y1) and B(x2, y2)?

Back

Front

If point C divides the segment AB in the ratio m:n, how do you find the coordinates of C?

Back

The coordinates of C are given by C = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)).

Front

What is the length of a line segment with endpoints (x1, y1) and (x2, y2)?

Back

Front

What are the coordinates of the midpoint of the segment joining (4, 7) and (1, 11)?

Back

The midpoint is M = ((4 + 1)/2, (7 + 11)/2) = (2.5, 9).

Front

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

Back

Use the section formula: C = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)).

Front

What is the significance of the ratio in dividing a line segment?

Back

The ratio indicates how the segment is divided into parts, affecting the position of the dividing point.

Front

What is the formula for finding the length of a segment between points (7, -1) and (-3, 3)?

Back

Front

What is the midpoint of the segment joining points (4, -2) and (-2, 5)?

Back

The midpoint is M = ((4 + (-2))/2, (-2 + 5)/2) = (1, 1.5).