Partitioning a Segment

Front

What is partitioning a segment in geometry?

Back

Partitioning a segment involves dividing a line segment into parts based on a specific ratio.

Front

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

Back

Use the formula: P = (x1 + k(x2 - x1), y1 + k(y2 - y1)), where k is the ratio part.

Front

If a segment is divided in the ratio 2:1, how many total parts are there?

Back

There are 3 total parts.

Front

What does it mean if a point is 2/3rds of the distance from point J to point K?

Back

It means the point is located closer to K, specifically at two-thirds of the way along the segment from J to K.

Front

True or False: A directed line segment MN partitioned into a ratio of 1:2 is the same as segment NM partitioned into a ratio of 2:1.

Back

True.

Front

What are the coordinates of the point that partitions segment AB in the ratio 5:1 with A(2, 4) and B(8, 10)?

Back

(7, 9) is the point that partitions segment AB in the ratio 5:1.

Front

What is the formula to calculate the coordinates of a point that divides a segment in the ratio m:n?

Back

P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)).

Front

If point A is at (2, 4) and point B is at (8, 10), what is the distance between A and B?

Back

The distance is √((8-2)² + (10-4)²) = √(36 + 36) = √72 = 6√2.

Front

What is the significance of the ratio in partitioning a segment?

Back

The ratio determines how the segment is divided into parts, influencing the location of the partition point.

Front

How do you express the ratio of a segment in simplest form?

Back

Divide both parts of the ratio by their greatest common divisor.