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).

Tags

CCSS.HSG.GPE.B.6

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).

Tags

CCSS.HSG.GPE.B.6

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).

Tags

CCSS.HSG.GPE.B.6

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.

Tags

CCSS.HSG.GPE.B.6

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).

Tags

CCSS.HSG.GPE.B.6

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).

Tags

CCSS.HSG.GPE.B.6

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.

Tags

CCSS.HSG.GPE.B.6

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.

Tags

CCSS.5.G.A.1

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).

Tags

CCSS.HSG.GPE.B.7

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.

Tags

CCSS.HSG.GPE.B.6