Coordinate Geometry - Distance & Section Formula for Exams

Coordinate Geometry - Distance and Section Formula - Problem Set

Q. If point A is at (1, 2) and point B is at (4, 6), what is the section formula ratio if point C divides AB in the ratio 1:2?

A. (2, 4)
B. (3, 5)
C. (2.5, 4)
D. (3, 4)

Solution

Using the section formula: C = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where m=1, n=2. C = ((1*4 + 2*1)/(1+2), (1*6 + 2*2)/(1+2)) = (2.67, 4).

Correct Answer: B — (3, 5)

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Q. If point D is at (5, 5) and point E is at (1, 1), what is the distance DE?

A. 4
B. 5
C. 6
D. 7

Solution

Using the distance formula: d = √((5 - 1)² + (5 - 1)²) = √(16 + 16) = √32 = 4√2 ≈ 5.66.

Correct Answer: B — 5

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Q. If point D is at (6, 8) and point E is at (2, 4), what is the length of DE?

A. 4.47
B. 5.66
C. 6.32
D. 7.21

Solution

Using the distance formula: d = √((6 - 2)² + (8 - 4)²) = √(16 + 16) = √32 = 5.66.

Correct Answer: B — 5.66

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Q. If point D is at (6, 8) and point E is at (2, 4), what is the section formula ratio if point F divides DE in the ratio 1:3?

A. (3, 5)
B. (4, 6)
C. (2.5, 4.5)
D. (3.5, 5.5)

Solution

Using the section formula: F = ((1*2 + 3*6)/(1+3), (1*4 + 3*8)/(1+3)) = (5, 7).

Correct Answer: A — (3, 5)

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Q. What is the coordinates of the point that divides the line segment joining (2, 3) and (10, 7) in the ratio 3:1?

A. (5, 4)
B. (6, 5)
C. (7, 6)
D. (8, 5)

Solution

Using the section formula: C = ((3*10 + 1*2)/(3+1), (3*7 + 1*3)/(3+1)) = (7.5, 5.25).

Correct Answer: B — (6, 5)

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Q. What is the coordinates of the point that divides the line segment joining (3, 2) and (9, 10) in the ratio 2:1?

A. (5, 4)
B. (6, 6)
C. (7, 8)
D. (8, 9)

Solution

Using the section formula: C = ((2*9 + 1*3)/(2+1), (2*10 + 1*2)/(2+1)) = (5, 4).

Correct Answer: A — (5, 4)

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Q. What is the coordinates of the point that divides the line segment joining (3, 4) and (9, 10) in the ratio 1:3?

A. (6, 8)
B. (5, 7)
C. (4, 6)
D. (7, 9)

Solution

Using the section formula: C = ((1*9 + 3*3)/(1+3), (1*10 + 3*4)/(1+3)) = (6, 8).

Correct Answer: A — (6, 8)

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Q. What is the midpoint of the line segment joining the points (10, 10) and (20, 20)?

A. (15, 15)
B. (10, 10)
C. (20, 20)
D. (25, 25)

Solution

Using the midpoint formula: M = ((10 + 20)/2, (10 + 20)/2) = (15, 15).

Correct Answer: A — (15, 15)

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Q. What is the midpoint of the line segment joining the points (6, 8) and (10, 12)?

A. (8, 10)
B. (7, 9)
C. (9, 10)
D. (6, 12)

Solution

Using the midpoint formula: M = ((6 + 10)/2, (8 + 12)/2) = (8, 10).

Correct Answer: A — (8, 10)

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Coordinate Geometry - Distance and Section Formula - Problem Set

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