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 is the x-coordinate of point P that divides AB in the ratio 2:5?

Back

Using the formula, P(x) = ((2*1 + 5*(-2))/(2+5) = (-8/7).

Front

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

Back

Using the formula, P(y) = ((2*3 + 5*6)/(2+5) = (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 is point P located?

Back

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

Front

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

Back

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

Front

How do you determine the ratio in which a point divides a line segment?

Back

The ratio can be determined by comparing the distances from the point to each endpoint of the segment.

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

Back

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

Front

How can you verify if a point lies on a line segment?

Back

Check if the point's coordinates satisfy the line equation and if they lie between the endpoints' coordinates.