Front

What is the formula to find the coordinates of a point that partitions a line segment in a given ratio?

Back

If A(x1, y1) and B(x2, y2) are the endpoints of the segment and the ratio is m:n, the coordinates of the point P that partitions AB in the ratio m:n are given by: P = ( (mx2 + nx1) / (m+n), (my2 + ny1) / (m+n) ).

Front

Given points A(-8,4) and B(16,-2), find the coordinates of the point that partitions the segment AB in the ratio 1:3.

Back

Using the formula, P = ( (1*16 + 3*(-8)) / (1+3), (1*(-2) + 3*4) / (1+3) ) = (-2, 2.5).

Front

What does it mean to partition a line segment in a ratio?

Back

Partitioning a line segment in a ratio means dividing the segment into parts that are proportional to the given ratio, determining the location of a point along the segment.

Front

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

Back

Use the section formula, which calculates the coordinates based on the endpoints and the ratio.

Front

If point A is at (-14,8) and point B is at (16,-2), what point P partitions AB in the ratio 3:2?

Back

Using the section formula, P = ( (3*16 + 2*(-14)) / (3+2), (3*(-2) + 2*8) / (3+2) ) = (4, 2).

Front

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

Back

The ratio indicates how the segment is divided, affecting the relative distances from the endpoints to the partition point.

Front

What is the expression for a point that partitions points M and P in the ratio 7:9?

Back

Front

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

Back

For points M and P, the point that divides the segment in the ratio m:n is given by: P = (m*P + n*M) / (m+n).

Front

What is the formula for finding the midpoint of a line segment?

Back

The midpoint M of a segment with endpoints A(x1, y1) and B(x2, y2) is given by: M = ( (x1 + x2) / 2, (y1 + y2) / 2 ).

Front

What is the distance formula between two points in a coordinate plane?

Back