Coordinate Geometry for Competitive Exam Success

Coordinate Geometry

Q. Find the area of the triangle formed by the points (0, 0), (4, 0), and (0, 3). (2022) 2022

A. 6
B. 12
C. 8
D. 10

Solution

Area = 1/2 * base * height = 1/2 * 4 * 3 = 6.

Correct Answer: A — 6

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Q. Find the coordinates of the centroid of the triangle with vertices (0, 0), (6, 0), and (0, 8). (2022)

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

Solution

Centroid = ((0+6+0)/3, (0+0+8)/3) = (2, 2).

Correct Answer: A — (2, 2)

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Q. Find the coordinates of the centroid of the triangle with vertices at (0, 0), (6, 0), and (0, 8).

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

Solution

Centroid = ((0+6+0)/3, (0+0+8)/3) = (2, 2).

Correct Answer: A — (2, 2)

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Q. Find the midpoint of the line segment joining the points (2, 3) and (4, 7). (2022) 2022

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

Solution

Midpoint = ((2+4)/2, (3+7)/2) = (3, 5).

Correct Answer: A — (3, 5)

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Q. If the coordinates of point A are (1, 2) and point B are (4, 6), what is the length of AB? (2023)

A. 5
B. 4
C. 3
D. 6

Solution

Length AB = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5.

Correct Answer: A — 5

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Q. If the coordinates of point C are (5, 5) and point D are (1, 1), what is the slope of CD? (2021)

A. 1
B. 0
C. 2
D. 3

Solution

Slope = (5-1)/(5-1) = 4/4 = 1

Correct Answer: A — 1

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Q. If the coordinates of point C are (5, 5) and point D are (5, 10), what is the distance CD? (2021)

A. 5
B. 10
C. 15
D. 20

Solution

Distance CD = |10 - 5| = 5.

Correct Answer: A — 5

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Q. If the coordinates of point C are (5, 5) and point D are (5, 10), what is the length of CD? (2021)

A. 5
B. 10
C. 15
D. 20

Solution

Length CD = |10 - 5| = 5.

Correct Answer: A — 5

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Q. If the coordinates of point C are (5, 5) and the slope of line AC is 1, what is the equation of line AC? (2021)

A. y = x
B. y = 5
C. y = x + 5
D. y = x - 5

Solution

Using point-slope form: y - 5 = 1(x - 5) => y = x

Correct Answer: A — y = x

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Q. If the coordinates of point C are (5, 5) and the slope of the line is 1, what is the equation of the line? (2021) 2021

A. y = x
B. y = 5
C. y = 2x - 5
D. y = x + 5

Solution

Using point-slope form: y - 5 = 1(x - 5) => y = x.

Correct Answer: A — y = x

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Q. What is the area of a rectangle with vertices at (1, 1), (1, 5), (4, 1), and (4, 5)? (2021)

A. 12
B. 15
C. 10
D. 8

Solution

Area = length * width = (4-1) * (5-1) = 3 * 4 = 12.

Correct Answer: A — 12

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Q. What is the coordinates of the centroid of the triangle with vertices (0, 0), (6, 0), and (3, 6)? (2022)

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

Solution

Centroid = ((0+6+3)/3, (0+0+6)/3) = (3, 2).

Correct Answer: A — (3, 2)

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Q. What is the distance between the points (-1, -1) and (2, 3)? (2022) 2022

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

Solution

Distance = √[(2 - (-1))² + (3 - (-1))²] = √[3² + 4²] = √25 = 5.

Correct Answer: A — 5

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Q. What is the distance between the points (-1, -1) and (2, 3)? (2023)

A. 5
B. 4
C. 3
D. 6

Solution

Distance = √[(2 - (-1))² + (3 - (-1))²] = √[3² + 4²] = √25 = 5.

Correct Answer: A — 5

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Q. What is the distance between the points (3, 4) and (7, 1)? (2021) 2021

A. 5
B. 4
C. 3
D. 6

Solution

Distance = √[(7-3)² + (1-4)²] = √[4 + 9] = √13 ≈ 5.

Correct Answer: A — 5

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Q. What is the distance from the point (1, 1) to the line x + y = 2? (2023)

A. 1
B. 2
C. 0
D. 3

Solution

Distance = |1 + 1 - 2| / √(1² + 1²) = 0 / √2 = 0.

Correct Answer: A — 1

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Q. What is the distance from the point (1, 2) to the line x + y - 3 = 0? (2023)

A. 1
B. 2
C. 3
D. 4

Solution

Distance = |1 + 2 - 3| / √(1² + 1²) = |0| / √2 = 0, closest option is 1.

Correct Answer: B — 2

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Q. What is the distance from the point (1, 2) to the line x + y = 5? (2020)

A. 3
B. 2
C. 1
D. 4

Solution

Distance = |1 + 2 - 5| / √(1² + 1²) = | -2 | / √2 = 2/√2 = √2.

Correct Answer: A — 3

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Q. What is the distance from the point (2, 3) to the line x + y - 5 = 0? (2022)

A. 1
B. 2
C. 3
D. 4

Solution

Distance = |(1*2 + 1*3 - 5)| / √(1² + 1²) = |5 - 5| / √2 = 0

Correct Answer: A — 1

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Q. What is the distance from the point (2, 3) to the line x + y = 5? (2020)

A. 1
B. 2
C. 3
D. 4

Solution

Distance = |(1*2 + 1*3 - 5)| / √(1² + 1²) = |5 - 5| / √2 = 0/√2 = 0

Correct Answer: B — 2

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Q. What is the distance from the point (3, 4) to the line x + y = 5? (2022)

A. 1
B. 2
C. 3
D. 4

Solution

Distance = |3 + 4 - 5| / √(1² + 1²) = |2| / √2 = 2/√2 = √2.

Correct Answer: B — 2

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Q. What is the equation of the line passing through (0, 0) and (2, 4)? (2019)

A. y = 2x
B. y = x
C. y = 4x
D. y = 3x

Solution

Slope = (4-0)/(2-0) = 2, so the equation is y = 2x.

Correct Answer: A — y = 2x

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Q. What is the equation of the line passing through (0, 0) with a slope of 3? (2021)

A. y = 3x
B. y = x/3
C. y = 3/x
D. y = 1/3x

Solution

Equation of line: y = mx + c; here m = 3, c = 0 => y = 3x

Correct Answer: A — y = 3x

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Q. What is the equation of the line passing through (2, 3) with a slope of 2? (2021)

A. y = 2x - 1
B. y = 2x + 1
C. y = 2x + 3
D. y = 2x - 3

Solution

Using point-slope form: y - 3 = 2(x - 2) => y = 2x - 4 + 3 => y = 2x - 1.

Correct Answer: B — y = 2x + 1

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Q. What is the length of the diagonal of a rectangle with vertices at (0, 0), (0, 3), (4, 0), and (4, 3)? (2022)

A. 5
B. 6
C. 7
D. 8

Solution

Diagonal = √[(4-0)² + (3-0)²] = √[16 + 9] = √25 = 5.

Correct Answer: A — 5

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Q. What is the length of the diagonal of a rectangle with vertices at (0, 0), (4, 0), (4, 3), and (0, 3)? (2021)

A. 5
B. 6
C. 7
D. 8

Solution

Length of diagonal = √[(4-0)² + (3-0)²] = √[16 + 9] = √25 = 5.

Correct Answer: A — 5

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Q. What is the length of the diagonal of a rectangle with vertices at (1, 1), (1, 4), (5, 1), and (5, 4)? (2021)

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

Solution

Diagonal length = √[(5-1)² + (4-1)²] = √[16 + 9] = √25 = 5.

Correct Answer: B — 5

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Q. What is the slope of the line passing through the points (1, 2) and (3, 6)? (2020) 2020

A. 2
B. 3
C. 1
D. 4

Solution

Slope = (6-2)/(3-1) = 4/2 = 2.

Correct Answer: A — 2

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Q. What is the slope of the line perpendicular to the line with slope 3?

A. -1/3
B. 1/3
C. 3
D. -3

Solution

Slope of perpendicular line = -1/m = -1/3.

Correct Answer: A — -1/3

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Q. What is the slope of the line perpendicular to the line y = 3x + 1? (2023)

A. -1/3
B. 1/3
C. 3
D. -3

Solution

Slope of perpendicular line = -1/(slope of original line) = -1/3.

Correct Answer: A — -1/3

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Showing 1 to 30 of 35 (2 Pages)

Coordinate Geometry

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