In this lesson, we will learn how to find the coordinates of a midpoint and an end point in three dimensions using a formula.

Q1:

Given that the midpoint of π΄ π΅ lies in the π₯ π¦ -plane, and the coordinates of π΄ and π΅ are ( β 1 2 , β 9 , π + 3 ) and ( β 1 5 , β 9 , 3 π ) , respectively, determine the value of π .

Q2:

Given that the midpoint of π΄ π΅ lies in the π₯ π§ -plane, and the coordinates of π΄ and π΅ are ( β 1 4 , π + 4 , β 1 9 ) and ( 1 7 , 2 π , 1 8 ) , respectively, determine the value of π .

Q3:

Given that the midpoint of π΄ π΅ lies in the π₯ π¦ -plane, and the coordinates of π΄ and π΅ are ( 3 , β 1 8 , π + 5 ) and ( 1 9 , 1 , 5 π ) , respectively, determine the value of π .

Q4:

Determine, to the nearest hundredth, the perimeter of the triangle formed by joining the midpoints of the sides of β³ π΄ π΅ πΆ , given that the coordinates of π΄ , π΅ , and πΆ are ( β 1 0 , β 8 , 2 ) , ( β 8 , β 7 , 1 0 ) , and ( β 2 , 3 , β 1 4 ) , respectively.

Q5:

Determine, to the nearest hundredth, the perimeter of the triangle formed by joining the midpoints of the sides of β³ π΄ π΅ πΆ , given that the coordinates of π΄ , π΅ , and πΆ are ( 1 9 , β 1 8 , 4 ) , ( 1 , β 4 , β 1 6 ) , and ( 1 3 , 1 8 , β 3 ) , respectively.

Q6:

Given that point ( 0 , 1 7 , β 1 0 ) is the midpoint of π΄ π΅ and that π΄ ( β 1 9 , 7 , 1 4 ) , what are the coordinates of π΅ ?

Q7:

Given that point ( β 9 , 1 7 , 1 1 ) is the midpoint of π΄ π΅ and that π΄ ( 4 , β 2 , 9 ) , what are the coordinates of π΅ ?

Q8:

Given that point ( β 1 , 4 , β 1 8 ) is the midpoint of π΄ π΅ and that π΄ ( 1 2 , 8 , β 1 ) , what are the coordinates of π΅ ?

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