Geometry Semester 1 Review

Front

What is the definition of a directed line segment?

Back

A directed line segment is a line segment that has a specific direction from one endpoint to another, often represented by points A and B.

Front

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

Back

Use the section formula: If point P divides the line segment AB in the ratio m:n, then the coordinates of P are given by P(x,y) = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)).

Front

What are the coordinates of the point that divides the segment from A(-18,-2) to B(0,6) in a ratio of 1:3?

Back

(-13.5, 0)

Front

What are the coordinates of the point that divides the segment from A(-5,-4) to B(5,1) in a ratio of 3:2?

Back

(-3, -1)

Front

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

Back

Distance = √((x2 - x1)² + (y2 - y1)²).

Front

What is the midpoint formula for a line segment with endpoints A(x1, y1) and B(x2, y2)?

Back

Midpoint M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the definition of a ratio in geometry?

Back

A ratio is a relationship between two quantities, indicating how many times the first number contains the second.

Front

What is the significance of the coordinates in a Cartesian plane?

Back

Coordinates represent the position of a point in a two-dimensional space, defined by an x-value (horizontal) and a y-value (vertical).

Front

What is the definition of a line segment?

Back

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

Front

What is the difference between a line and a line segment?

Back

A line extends infinitely in both directions, while a line segment has two endpoints and a finite length.