# Lesson Worksheet: Partitioning a Line Segment on the Coordinate Plane Mathematics

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

• A, ,
• B, ,
• C, ,
• D, ,

Q3:

If and , then divides by the ratio .

• 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:

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

Q6:

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

• A
• B
• C
• D

Q7:

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

• A
• B
• C
• D

Q8:

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

• A
• B
• C
• D

Q9:

Points , , , and have coordinates , , , and , respectively. is the midpoint of , and divides externally by the ratio , find the length of to the nearest hundredth, considering a length unit .

Q10:

Fill in the blank: Given that and , the divides in the ratio .

• A
• B
• C
• D

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