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In this lesson, we will learn how to find the coordinates of the midpoint between two points or those of an endpoint on the coordinate plane.

Q1:

Given π΄ ( 4 , 8 ) and π΅ ( 6 , 6 ) , what are the coordinates of the midpoint of π΄ π΅ ?

Q2:

Given π΄ ( 2 , 1 ) and πΆ ( β 8 , β 9 ) , what are the coordinates of π΅ , if πΆ is the midpoint of π΄ π΅ ?

Q3:

Consider the points π΄ ( π₯ , 7 ) , π΅ ( β 4 , π¦ ) , and πΆ ( 2 , 5 ) . Given that πΆ is the midpoint of π΄ π΅ , find the values of π₯ and π¦ .

Q4:

The origin is the midpoint of the straight segment π΄ π΅ . Find the coordinates of point π΅ if the coordinates of point π΄ are ( β 6 , 4 ) .

Q5:

Consider the points π΄ ( 7 , 7 ) , π΅ ( 9 , β 7 ) , and πΆ ( 5 , 1 ) . Given that π΄ π· is a median of the triangle π΄ π΅ πΆ and π is the midpoint of this median, determine the coordinates of π· and π .

Q6:

π΄ , π΅ , πΆ , and π· are collinear points. Suppose that the coordinates of points π΄ and πΆ are ( 2 , 4 ) and ( β 8 , β 8 ) , respectively, and that π΄ π΅ = π΅ πΆ = πΆ π· . What are the coordinates of π΅ and π· ?

Q7:

If πΆ ( β 5 , 4 ) is the midpoint of ο π΄ π΅ , where π΄ ( π₯ , 4 ) , π΅ ( β 5 , π¦ ) , find the values of π₯ and π¦ .

Q8:

πΆ is the midpoint of π΄ π΅ . Find the values of π₯ and π¦ if the coordinates of π΄ , π΅ , and πΆ are ( π₯ , 4 ) , ( 3 , β 2 ) , and ( 9 , π¦ ) respectively.

Q9:

The coordinates of the points π΄ , π΅ , and πΆ in the parallelogram π΄ π΅ πΆ π· are ( β 2 , β 5 ) , ( β 5 , β 7 ) , and ( β 1 , β 1 3 ) , respectively. If the point πΈ lies on ο« π΄ π· such that π΄ πΈ = 2 π΄ π· , determine the coordinates of the points π· and πΈ .

Q10:

The point πΆ is on ray ο π΄ π΅ but not segment π΄ π΅ , and its distance from π΄ ( 3 , 0 ) is 2 times its distance from π΅ ( β 9 , β 6 ) . What are its coordinates?

Q11:

Find the values of π and π so that ( β 2 π , 2 π + π ) is the midpoint of the line segment between ( β 2 , β 3 ) and ( 2 , 1 1 ) .

Q12:

Find the point π΄ on the π₯ -axis and the point π΅ on the π¦ -axis such that οΌ 3 2 , β 5 2 ο is the midpoint of π΄ π΅ .

Q13:

Point ( 2 , β 7 ) is the midpoint of the line segment on endpoints ( π₯ , β 9 ) and ( 1 , π¦ ) . What is π₯ + π¦ ?

Q14:

π΄ ( 3 , 1 7 ) , πΉ ( 1 0 , 1 7 ) , π΅ ( 1 7 , 1 7 ) , π· ( 4 , 8 . 5 ) , and πΆ ( 1 8 . 5 , 4 . 2 5 ) are points on the trapezoid π΄ π΅ πΆ π· . If πΉ πΊ is parallel to π΄ π· , what is the π₯ -coordinate of point πΊ ?

Q15:

Suppose the circle of centre π οΌ β 4 , 1 2 ο and diameter π΄ π΅ , where π΅ ( β 3 , 0 ) . Find the coordinates of π΄ , and give the circumference to two decimal places.

Q16:

A rectangular garden is next to a house along a road. In the garden is an orange tree 7 m from the house and 3 m from the road. There is also an apple tree, 5 m from the house and 9 m from the road. A fountain is placed halfway between the trees. How far is the fountain from the house and the road?

Q17:

Consider the two points π΄ ( π₯ , π¦ ) ο§ ο§ and π΅ ( π₯ , π¦ ) ο¨ ο¨ .

Find an expression for the midpoint of the line segment π΄ π΅ .

π΄ and π΅ have the coordinates ( 1 , 1 ) and ( 3 , β 5 ) respectively. Find the midpoint of the line segment π΄ π΅ .

Q18:

On the graph, which point is halfway between ( 1 , 8 ) and ( 5 , 2 ) ?

Q19:

Points π΄ and π΅ have coordinates ( 3 , 3 ) and ( β 2 , β 5 ) respectively. Is the point οΌ 1 2 , β 1 ο the midpoint of segment π΄ π΅ ?

Q20:

Let π΄ ( β 3 , β 8 ) , π΅ ( β 3 , 6 ) , and πΆ ( 3 , β 8 ) be the vertices of a triangle. Suppose that point π· on π΅ πΆ is such that ο« π΄ π· bisects the angle at π΄ . What is the point π· ?

Q21:

Two points π΄ and π΅ are at ( 1 , 3 ) and ( β 2 , β 5 ) respectively. Point πΆ lies on the line segment π΄ π΅ such that the lengths of π΄ πΆ and πΆ π΅ are equal. Find the coordinates of πΆ .

Q22:

If the coordinates of the points π΄ and π΅ are ( 2 , 9 ) and ( β 8 , 1 ) respectively, find the midpoint of π΄ π΅ .

Q23:

Which number is at the midpoint of π΄ π΅ ?

Q24:

If πΆ is the midpoint of π΄ π΅ , find the values of π₯ and π¦ if the coordinates of π΄ , π΅ , and πΆ are ( 9 , β 7 ) , ( 5 , β 5 ) , and ( π₯ , π¦ ) respectively.

Q25:

Suppose that π΄ ( 6 , 1 0 ) and π΅ ( 6 , 1 5 ) . What is the midpoint of π΄ π΅ ?

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