Practice Internal Division (3.1) - Three Dimensional Geometry - ICSE 12 Mathematics

Practice: Internal Division

Lesson 3.1Three Dimensional Geometry

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9 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the midpoint of the points (1, 1, 1) and (3, 3, 3)?
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Calculate the average of each coordinate.
Question 2.
Find the coordinates of a point R that divides the segment PQ where P(0, 0, 0) and Q(2, 2, 2) in the ratio 1:1.
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Use the section formula for m=n.
3Question 3.
What is the formula for the section formula in 3D?
- A) R = (mx2 + nx1)/(m+n), (my2 + ny1)/(m+n), (mz2 + nz1)/(m+n)
- B) R = (mx1 + ny2)/(m-n), (my1 + ny2)/(m-n)
- C) R = (x1+x2)/2, (y1+y2)/2, (z1+z2)/2
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Think about the coordinates and their respective weights in the ratio.
4Question 4.
The midpoint of the points (2, 4, 6) and (8, 10, 12) is?
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Add the coordinates and divide by 2.
Question 5.
Find the coordinates of a point R that divides the segment joining points A(1, 1, 1) and B(6, 6, 6) in the ratio 5:2.
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Keep in mind the section formula - calculate for each axis separately!
Question 6.
A point C divides the line segment connecting D(4, -2, 1) and E(-6, 3, 5) in the ratio 3:4. What are the coordinates of point C?
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Split the calculations into separate components for clarity.

5 more questions in this section. Enroll free to practise them all.