# Worksheet: Coordinates of a Point in a Cartesian Plane

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:

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

• A
• B
• C
• D

Q3:

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

• A
• B
• C
• D

Q4:

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

• A
• B
• C
• D

Q5:

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

Q6:

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

Q7:

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.

• A internal division by ratio , external division by ratio
• B internal division by ratio , external division by ratio
• C internal division by ratio , external division by ratio
• D internal division by ratio , external division by ratio

Q8:

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.

• A internal division by ratio , external division by ratio
• B internal division by ratio , external division by ratio
• C internal division by ratio , external division by ratio
• D internal division by ratio , external division by ratio

Q9:

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

Q10:

A bus is travelling 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 ,

Q11:

Given points and , find the ratio by which the -axis 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,

Q12:

Given and , find the coordinates of on for which .

• A ,
• B ,
• C ,
• D ,

Q13:

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

• A ,
• B ,
• C ,
• D ,

Q14:

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

Q15:

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

• A
• B
• C
• D

Q16:

Find the ratio by which the -axis 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,

Q17:

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

• A
• B
• C
• D

Q18:

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

• A , ,
• B , ,
• C , ,
• D , ,

Q19:

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

• A
• B
• C
• D

Q20:

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