# Worksheet: Partitioning a Line Segment on the Coordinate Plane

In this worksheet, we will practice finding the coordinates of a point that divides a line segment on the coordinate plane with a ratio using the section formula.

Q1:

If the coordinates of and are and respectively, find the coordinates of the point that divides internally by the ratio .

• A
• B
• C
• D

Q2:

The coordinates of points and are and respectively. Given that intersects the -axis at and the -axis at , find the ratio by which is divided by points and respectively showing the type of division in each case.

• Ainternal division by ratio , external division by ratio
• Binternal division by ratio , external division by ratio
• Cinternal division by ratio , external division by ratio
• Dinternal division by ratio , external division by ratio

Q3:

The coordinates of and are and respectively. Determine the coordinates of the points that divide into four equal parts.

• A, ,
• B, ,
• C, ,
• D, ,

Q4:

A bus is traveling from city to city . Its first stop is at , which is halfway between the cities. Its second stop is at , which is two-thirds of the way from to . What are the coordinates of and ?

• A,
• B,
• C,
• D,

Q5:

Given and , what are the points and that divide into three parts of equal length?

• A,
• B,
• C,
• D,

Q6:

Consider and . Find the coordinates of , given that is on the ray but NOT on the segment and .

• A
• B
• C
• D

Q7:

Consider points and . Find the coordinates of , given that is on the ray but NOT on the segment and .

• A
• B
• C
• D

Q8:

Given and , find the coordinates of on for which .

• A,
• B,
• C,
• D,

Q9:

The coordinates of the points and are and respectively. Determine the coordinates of the point , given that it divides externally in the ratio .

• A
• B
• C
• D

Q10:

Suppose and another point , and that divides internally in the ratio . What are the coordinates of ?

• A
• B
• C
• D

Q11:

Line segment is a median in , where and . Find the point of intersection of the medians of the triangle .

• A
• B
• C
• D

Q12:

Find the ratio by which the divides the line segment , joining points and , showing the type of division, and determine the coordinates of the point of division.

• A internally,
• B internally,
• C externally,
• D externally,

Q13:

Given that the coordinates of the points and are and respectively, determine, in vector form, the coordinates of the point , which divides internally in the ratio .

• A
• B
• C
• D

Q14:

Given points and , find the ratio by which the divided line segment , together with the type of division. Determine the coordinates of the point of intersection.

• A externally,
• B externally,
• C internally,
• D internally,

Q15:

If the coordinates of the points and are and , respectively, find the ratio by which the point divides stating whether it is divided internally or externally, then determine the value of .

• A  externally,
• B  externally,
• C  internally,
• D  internally,

Q16:

If and , find in vector form the coordinates of point which divides externally in the ratio .

• A
• B
• C
• D

Q17:

If , , , , is the midpoint of , and divides externally by the ratio , find the length of to the nearest hundredth considering a length unit .

Q18:

If the coordinates of and are and respectively, find the coordinates of the point that divides internally by the ratio .

• A
• B
• C
• D

Q19:

The coordinates of the points and are and respectively. Determine the coordinates of the point , given that it divides externally in the ratio .

• A
• B
• C
• D

Q20:

The coordinates of points and are and respectively. Given that intersects the -axis at and the -axis at , find the ratio by which is divided by points and respectively showing the type of division in each case.

• Ainternal division by ratio , external division by ratio
• Binternal division by ratio , external division by ratio
• Cinternal division by ratio , external division by ratio
• Dinternal division by ratio , external division by ratio

Q21:

Two points and are at and respectively. Point lies on the line segment such that the length of is of . Find the coordinates of .

• A
• B
• C
• D
• E

Q22:

Two points and are at and respectively. Point lies on the line segment such that the length of is of . Find the coordinates of .

• A
• B
• C
• D
• E

Q23:

Two points and are at and respectively. Point lies on the line segment such that the lengths of and are in the ratio of . Find the coordinates of .

• A
• B
• C
• D
• E

Q24:

Two points and are at and respectively. Point lies on the line segment such that the lengths of and are in the ratio of . Find the coordinates of .

• A
• B
• C
• D
• E

Q25:

A quadrilateral has its vertices at the points , , , and . A point lies on such that the lengths of and are in the ratio of , and a point lies on such that the lengths of and are in the ratio of .

Find the coordinates of .

• A
• B
• C
• D
• E

Find the coordinates of .

• A
• B
• C
• D
• E

Find the slope of the line .

Find the equation of the line , giving your answer in the form .

• A
• B
• C
• D
• E