Geometry: Partitioning Line Segments

Questions and Answers

Find the coordinates of P so that P partitions the segment AB in the ratio of 5:1 if A(2,4) and B(8,10).

(7,9)

Find the coordinates of P so that P partitions the segment AB in the ratio of 1 to 3 if A(-5,4) and B(7,-4).

(-2,6)

Given the points M(-1,2) and N(7,14), find the coordinates of the point Q on directed line MN that partitions MN in the ratio of 1:3.

(1,5)

Given the points J(-1,2) and K(5,2), find the coordinates of the point L on directed line JK that partitions JK in the ratio of 1:2.

(1,2) Signup and view all the answers

Given the points A(-3,-4) and B(5,0), find the coordinates of the point P on directed line AB that partitions AB in the ratio of 2:3.

(0.2,-2.4) Signup and view all the answers

Determine the point P that partitions the directed line segment AB into a ratio of 1:3, where A(-2,-5) and B(6,-1).

(0,-4) Signup and view all the answers

Determine the point P that partitions the directed line segment AB into a ratio of 1:3, where A(2,-6) and B(6,-10).

(3,-5) Signup and view all the answers

Find the point P that partitions the directed line segment from (-3, -2) to (4,8) into a ratio of 3:2.

(1.2,4) Signup and view all the answers

Line segment RW has endpoints R(-4,5) and W(6,20). Point P is on RW such that RP:PW is 2:3. What are the coordinates of P?

(0,11) Signup and view all the answers

Point M is on JK such that JM:MK is 2:3. If J has coordinates of (3,5) and K has coordinates of (8,-5), the coordinates of M are:

(5,9) Signup and view all the answers

Directed line segment AB has endpoints A(-8,-8) and B(2,7). Point P is on AB such that AP:PB is 2:3. What are the coordinates of point P?

(-4,-2) Signup and view all the answers

Find the coordinates of P so that P partitions AB in a ratio of 3:4 with A(-9,-9) and B(5,-2).

(-3,-6) Signup and view all the answers

Study Notes

Partitioning Line Segments

Points A and B are used as endpoints for segments needing partitioning.
P represents the point dividing the segment in specified ratios.

Ratios and Coordinates

P partitions segment AB in a ratio of 5:1 for A(2,4) and B(8,10), resulting in coordinates (7,9).
Using A(-5,4) and B(7,-4) to find partition P in a ratio of 1:3 yields coordinates (-2,6).
Given M(-1,2) and N(7,14), point Q partitions MN in the ratio of 1:3, resulting in coordinates (1,5).
For points J(-1,2) and K(5,2) partitioned in a 1:2 ratio, L's coordinates are (1,2).
A(-3,-4) and B(5,0) give point P coordinates (0.2, -2.4) for a 2:3 ratio.
The directed segment from A(-2,-5) to B(6,-1) gives P coordinates (0,-4) in a 1:3 ratio.
In segment AB, A(2,-6) and B(6,-10) yield P coordinates (3,-5) at a 1:3 ratio.
From points (-3,-2) to (4,8), point P coordinates (1.2, 4) partition in a ratio of 3:2.
Endpoint coordinates R(-4,5) and W(6,20) with RP:PW in a 2:3 ratio give point P at (0,11).
For points J(3,5) and K(8,-5), point M divides in a 2:3 ratio, resulting in coordinates (5,9).
Segments with A(-8,-8) and B(2,7) partitioned in a ratio of 2:3 lead to P at (-4,-2).
Lastly, A(-9,-9) and B(5,-2) give P coordinates (-3,-6) for a ratio of 3:4.

Description

This quiz focuses on finding coordinates that partition line segments in given ratios. You'll work with different endpoints and ratios to determine the required points on the segments. Test your understanding of geometry concepts related to line segments and ratios!