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In this lesson, we will learn how to find the coordinates of a point that divides a line segment on the coordinate plane with a ratio.

Q1:

If the coordinates of π΄ and π΅ are ( 5 , 5 ) and ( β 1 , β 4 ) respectively, find the coordinates of the point πΆ that divides ο π΄ π΅ internally by the ratio 2 βΆ 1 .

Q2:

If the coordinates of π΄ and π΅ are ( 3 , 1 ) and ( β 7 , 1 ) respectively, find the coordinates of the point πΆ that divides ο π΄ π΅ internally by the ratio 2 βΆ 3 .

Q3:

Consider π΄ ( β 1 , β 2 ) and π΅ ( β 7 , 7 ) . Find the coordinates of πΆ , given that πΆ is on the ray ο« π΄ π΅ but NOT on the segment π΄ π΅ and π΄ πΆ = 2 πΆ π΅ .

Q4:

Line segment π΄ π· is a median in β³ π΄ π΅ πΆ , where π΄ = ( 8 , β 7 ) and π· = ( 2 , β 1 ) . Find the point of intersection of the medians of the triangle π΄ π΅ πΆ .

Q5:

The coordinates of the points π΄ and π΅ are ( β 3 , 4 ) and ( β 4 , β 2 ) respectively. Determine the coordinates of the point πΆ , given that it divides ο« π΄ π΅ externally in the ratio 2 βΆ 1 .

Q6:

The coordinates of the points π΄ and π΅ are ( 2 , 2 ) and ( 5 , 1 ) respectively. Determine the coordinates of the point πΆ , given that it divides ο« π΄ π΅ externally in the ratio 4 βΆ 3 .

Q7:

The coordinates of points π΄ and π΅ are ( 4 , 4 ) and ( 1 , β 2 ) respectively. Given that β ο© ο© ο© ο© β π΄ π΅ intersects the π₯ -axis at πΆ and the π¦ -axis at π· , find the ratio by which ο π΄ π΅ is divided by points πΆ and π· respectively showing the type of division in each case.

Q8:

The coordinates of points π΄ and π΅ are ( 6 , 6 ) and ( 1 , β 4 ) respectively. Given that β ο© ο© ο© ο© β π΄ π΅ intersects the π₯ -axis at πΆ and the π¦ -axis at π· , find the ratio by which ο π΄ π΅ is divided by points πΆ and π· respectively showing the type of division in each case.

Q9:

Given that the coordinates of the points π΄ and π΅ are ( 9 , 6 ) and ( β 1 , 6 ) respectively, determine, in vector form, the coordinates of the point πΆ , which divides ο π΄ π΅ internally in the ratio 4 βΆ 1 .

Q10:

A bus is travelling from city π΄ ( 1 0 , β 1 0 ) to city π΅ ( β 8 , 8 ) . Its first stop is at πΆ , which is halfway between the cities. Its second stop is at π· , which is two-thirds of the way from π΄ to π΅ . What are the coordinates of πΆ and π· ?

Q11:

Given points π΄ ( β 2 , β 6 ) and π΅ ( β 7 , 4 ) , find the ratio by which the π₯ -axis divided line segment π΄ π΅ , together with the type of division. Determine the coordinates of the point of intersection.

Q12:

Given π΄ ( 6 , β 6 ) and π΅ ( β 7 , β 1 ) , find the coordinates of πΆ on β ο© ο© ο© ο© β π΄ π΅ for which 2 π΄ πΆ = 9 πΆ π΅ .

Q13:

Given π΄ ( β 5 , 9 ) and π΅ ( 7 , β 3 ) , what are the points πΆ and π· that divide π΄ π΅ into three parts of equal length?

Q14:

If the coordinates of the points π΄ and π΅ are ( 9 , β 1 ) and ( 2 , β 1 ) , respectively, find the ratio by which the point πΆ ( 7 , π¦ ) divides π΄ π΅ stating whether it is divided internally or externally, then determine the value of π¦ .

Q15:

Consider points π΄ ( 2 , 3 ) and π΅ ( β 4 , β 3 ) . Find the coordinates of πΆ , given that πΆ is on the ray ο« π΅ π΄ but NOT on the segment π΄ π΅ and π΄ πΆ = 2 π΄ π΅ .

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.

Q17:

Suppose π΄ ( 1 , 3 ) and another point π΅ , and that πΆ ( 5 , 1 ) divides π΄ π΅ internally in the ratio 2 βΆ 3 . What are the coordinates of π΅ ?

Q18:

The coordinates of π΄ and π΅ are ( 1 , 9 ) and ( 9 , 9 ) respectively. Determine the coordinates of the points that divide π΄ π΅ into four equal parts.

Q19:

If π΄ ( 3 , β 2 ) and π΅ ( β 2 , 4 ) , find in vector form the coordinates of point πΆ which divides ο π΄ π΅ externally in the ratio 4 βΆ 3 .

Q20:

If π΄ ( β 1 5 , β 7 ) , π΅ ( 7 , 2 ) , πΆ ( 4 , β 1 7 ) , π· ( 1 3 , β 2 ) , πΈ is the midpoint of π΄ π΅ , and π divides πΆ π· externally by the ratio 7 βΆ 4 , find the length of πΈ π to the nearest hundredth considering a length unit = 1 c m .

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