Coordinate Geometry - Distance & Section Formula for Exams

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Coordinate Geometry - Distance and Section Formula - Coordinate Geometry Applications - Problem Set

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

A. (2, 4)
B. (3, 5)
C. (2.5, 4)
D. (3.5, 5)

Solution

Using the section formula: C = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) = ((1*4 + 2*1)/(1+2), (1*6 + 2*2)/(1+2)) = (3, 5).

Correct Answer: B — (3, 5)

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Q. If point D divides the line segment joining points (2, 5) and (8, 9) in the ratio 3:1, what are the coordinates of point D?

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

Solution

Using the section formula: D = ((3*8 + 1*2)/(3+1), (3*9 + 1*5)/(3+1)) = (5, 7).

Correct Answer: A — (5, 7)

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Q. If point E is at (3, 4) and point F is at (6, 8), what is the distance between E and F?

A. 3
B. 5
C. 6
D. 7

Solution

Using the distance formula: d = √((6 - 3)² + (8 - 4)²) = √(9 + 16) = √25 = 5.

Correct Answer: B — 5

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Q. If point P is at (3, 5) and point Q is at (9, 1), what is the coordinates of point R that divides PQ in the ratio 2:3?

A. (5.4, 3.6)
B. (6, 4)
C. (5, 4)
D. (4, 3)

Solution

Using the section formula: R = ((2*9 + 3*3)/(2+3), (2*1 + 3*5)/(2+3)) = (5.4, 3.6).

Correct Answer: A — (5.4, 3.6)

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Q. What is the coordinates of the point that divides the line segment joining (6, 8) and (10, 12) in the ratio 1:3?

A. (8, 10)
B. (7, 9)
C. (9, 11)
D. (6.5, 8.5)

Solution

Using the section formula: C = ((1*10 + 3*6)/(1+3), (1*12 + 3*8)/(1+3)) = (8, 10).

Correct Answer: A — (8, 10)

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