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Test: Section Formula - SAT MCQ


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10 Questions MCQ Test - Test: Section Formula

Test: Section Formula for SAT 2024 is part of SAT preparation. The Test: Section Formula questions and answers have been prepared according to the SAT exam syllabus.The Test: Section Formula MCQs are made for SAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Section Formula below.
Solutions of Test: Section Formula questions in English are available as part of our course for SAT & Test: Section Formula solutions in Hindi for SAT course. Download more important topics, notes, lectures and mock test series for SAT Exam by signing up for free. Attempt Test: Section Formula | 10 questions in 15 minutes | Mock test for SAT preparation | Free important questions MCQ to study for SAT Exam | Download free PDF with solutions
Test: Section Formula - Question 1
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The coordinates of a point dividing the line segment joining (1, 2, 3) and (4, 5, 6) internally in the ratio 2:1 is _______.

Detailed Solution for Test: Section Formula - Question 1

The coordinates of a point dividing the line segment joining (x1, y1, z1) and (x2, y2, z2) internally in the ratio m : n is 
So, the coordinates of a point dividing the line segment joining (1, 2, 3) and (4, 5, 6) internally in the ratio 2:1 is 

Test: Section Formula - Question 2
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The coordinates of a point dividing the line segment joining (1, 2, 3) and (4, 5, 6) externally in the ratio 2:1 is __________.

Detailed Solution for Test: Section Formula - Question 2

The coordinates of a point dividing the line segment joining (x1, y1, z1) and (x2, y2, z2) externally in the ratio m : n is 
So, the coordinates of a point dividing the line segment joining (1, 2, 3) and (4, 5, 6) externally in the ratio 2:1 is = (7, 8, 9).

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Test: Section Formula - Question 3
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The ratio in which line joining (1, 2, 3) and (4, 5, 6) divide X-Y plane is ________

Detailed Solution for Test: Section Formula - Question 3

The coordinates of a point dividing the line segment joining (x1, y1, z1) and (x2, y2, z2) internally in the ratio m : n is 
Let ratio be k : 1.
So, z-coordinate of the point will be (k*6 + 1*3)/(k + 1).
We know, for X-Y plane, z coordinate is zero.
(6k + 1 * 3)/(k+1) = 0 ⇒ k = -1/2

Test: Section Formula - Question 4
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Find the points which trisects the line joining (4, 9, 8) and (13, 27, -4).
Detailed Solution for Test: Section Formula - Question 4

Points which trisect the line divides it into 2:1 and 1:2.
The coordinates of a point dividing the line segment joining (x1, y1, z1) and (x2, y2, z2) internally in the ratio m : n is 
For 1:2, coordinates of point are= (7, 15, 4)
For 2:1, coordinates of point are= (10, 21, 0)

Test: Section Formula - Question 5
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If P (2, 3, 9), Q (2, 5, 5) and R (8, 5, 3) are vertices of a triangle then find the length of median through Q.
Detailed Solution for Test: Section Formula - Question 5

We know, midpoint of (x1, y1, z1) and (x2, y2, z2) is ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2).
Midpoint of line PR is (5, 4, 6).
Length of median through Q is distance between midpoint of PR and Q i.e.

Test: Section Formula - Question 6
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Find midpoint of (1, 4, 6) and (5, 8, 10).
Detailed Solution for Test: Section Formula - Question 6

We know, midpoint of (x1, y1, z1) and (x2, y2, z2) is (x1+x2) /2, (y1+y2) /2, (z1+z2)/2).
So, midpoint of (1, 4, 6) and (5, 8, 10) is ((1+5)/ 2, (4+8)/ 2, (6+10)/2) is (3, 6, 8).

Test: Section Formula - Question 7
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In which ratio (3, 4, 5) divides the line segment joining (1, 2, 3) and (4, 5, 6) internally?
Detailed Solution for Test: Section Formula - Question 7

The coordinates of a point dividing the line segment joining (x1, y1, z1) and (x2, y2, z2) internally in the ratio m: n is 
Let the ratio be k : 1.So, the coordinates of a point dividing the line segment joining (1, 2, 3) and (4, 5, 6) internally in the ratio k: 1 is

⇒ (4k + 1)/(k + 1) = 3
⇒ 4k + 1 = 3k + 3
⇒ k = 2
So, ratio is 2:1.

Test: Section Formula - Question 8
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If coordinates of vertices of a triangle are (7, 6, 4), (5, 4, 6), (9, 5, 8), find the coordinates of centroid of the triangle.
Detailed Solution for Test: Section Formula - Question 8

If coordinates of vertices of a triangle are (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) the coordinates of centroid of the triangle are ((x1+x2+x3)/3, (y1+y2+y3)/3, (z1+z2+z3)/3)
So, coordinates of centroid of the given triangle are ((7 + 5 + 9)/3, (6 + 4 + 5)/3, (4 + 6 + 8)/3) = (7, 5, 3).

Test: Section Formula - Question 9
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Find the points which trisects the line joining (4, 9, 8) and (13, 27, -4).
Detailed Solution for Test: Section Formula - Question 9

Points which trisect the line divides it into 2:1 and 1:2.
The coordinates of a point dividing the line segment joining (x1, y1, z1) and (x2, y2, z2) internally in the ratio m : n is 
For 1:2, coordinates of point are = (7, 15, 4)
For 2:1, coordinates of point are = (10, 21, 0)

Test: Section Formula - Question 10
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If P (2, 3, 9), Q (2, 5, 5) and R (8, 5, 3) are vertices of a triangle then find the length of median through P.
Detailed Solution for Test: Section Formula - Question 10

We know, midpoint of (x1, y1, z1) and (x2, y2, z2) is ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2).
Midpoint of line QR is (5, 5, 4).
Length of median through P is distance between midpoint of QR and P i.e. 

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