Topic 3&4 q. 8

Front

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

Back

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)) where A(x1,y1) and B(x2,y2).

Front

Given points A(-2, 6) and B(1, 3), what are the coordinates of point P that divides AB in the ratio 2:5?

Back

P = (-8/7, 36/7).

Front

What does it mean for a point to divide a line segment in a ratio?

Back

It means that the point divides the segment into two parts that are proportional to the given ratio.

Front

If point P divides line segment AB in the ratio 1:1, where A and B are endpoints, what is the location of P?

Back

P is the midpoint of AB, calculated as P = ((x1+x2)/2, (y1+y2)/2).

Front

How do you calculate the distance between two points A(x1, y1) and B(x2, y2)?

Back

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

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-axis and a y-axis.

Front

What is the ratio of the segments AP and PB if P divides AB in the ratio 2:5?

Back

AP:PB = 2:5.

Front

How do you express a point's location in a coordinate system?

Back

A point's location is expressed as an ordered pair (x, y), where x is the horizontal position and y is the vertical position.

Front

What is the concept of a weighted average in the context of dividing a line segment?

Back

A weighted average takes into account the ratio in which a segment is divided, giving more 'weight' to one endpoint based on the ratio.

Front

If point P divides line segment AB in the ratio 3:2, how would you find the coordinates of P?

Back

Use the formula P = ((3*x2 + 2*x1)/(3+2), (3*y2 + 2*y1)/(3+2)).