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In this lesson, we will learn how to find the coordinates of a point in three dimensions, the plane in which it is located, and the distance between two points.

Q1:

Find the distance between the two points π΄ ( β 7 , 1 2 , 3 ) and π΅ ( β 4 , β 1 , β 8 ) .

Q2:

Given that π΄ ( π , π , π ) is the midpoint of the line segment between π΅ ( 9 , β 1 7 , 2 ) and πΆ ( 1 6 , β 1 2 , 7 ) , what is π + π + π ?

Q3:

Given that πΆ οΌ β 1 2 , 0 , β 2 ο is the midpoint of π΄ π΅ , where the coordinates of π΄ and π΅ are ( π + 5 , 8 , π + 4 ) and ( β 6 , π + 7 , 5 ) , respectively, what is π + π β π ?

Q4:

Given that point ( 5 π , π + 2 , β 1 4 ) lies in the π₯ π§ -plane, determine its distance from the π¦ π§ -plane.

Q5:

Calculate, to two decimal places, the area of the triangle π π π , where the coordinates of its vertices are at π ( 4 , 0 , 2 ) , π ( 2 , 1 , 5 ) , and π ( β 1 , 0 , 1 ) .

Q6:

What is the distance between the point ( 1 9 , 5 , 5 ) and the π₯ -axis?

Q7:

The points π΄ , π΅ , and πΆ are on the π₯ -, π¦ -, and π§ -axes, respectively. Given that ( 1 2 , β 1 2 , 0 ) is the midpoint of π΄ π΅ and ( 0 , β 1 2 , β 1 4 ) the midpoint of π΅ πΆ , find the coordinates of the midpoint of π΄ πΆ .

Q8:

Find π so that the points ( 3 , 9 , β 4 ) , ( 9 , β 3 , β 1 ) , ( β 7 , 2 9 , π ) are collinear.

Q9:

Given that point ( π + 3 , 4 π , 1 9 ) lies in the π¦ π§ -plane, determine its distance from the π₯ π§ -plane.

Q10:

Given that point ( 2 , 6 π , π + 3 ) lies in the π₯ π¦ -plane, determine its distance from the π₯ π§ -plane.

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