alleryThe distance of the point $(3,4)$ from the line $3x + 4y - 5 = 0$ is:
- 5
- 4
- 2
- $\tfrac{20}{7}$
Show answer and solution
Correct answer: B. 4
We have d = |3·3 + 4·4 − 5| / √(3²+4²).
That is d = |9+16−5|/5.
That is d = 20/5.
So d = 4.
GRE Straight Lines and Conic Sections — practice questions — page 2
Explore 49 free Straight Lines and Conic Sections questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 31–49 of 49.
The distance of the point $(3,4)$ from the line $3x + 4y - 5 = 0$ is:Read the answer and worked solution →The x-intercept of the line $2x + 3y = 12$ is:Read the answer and worked solution →The slope of a line perpendicular to $y = 3x + 2$ is:Read the answer and worked solution →The slope of a vertical line (parallel to the y-axis) is:Read the answer and worked solution →A line passes through the origin and the point $(2,2)$. The angle it makes with the positive x-axis is:Read the answer and worked solution →The slope of the line passing through the points (x₁, y₁) and (x₂, y₂) (where x₁ ≠ x₂) isRead the answer and worked solution →The slope of a horizontal line isRead the answer and worked solution →The equation of a line passing through the origin with slope m isRead the answer and worked solution →Two lines with slopes m₁ and m₂ are PARALLEL if and only ifRead the answer and worked solution →Two lines with slopes m₁ and m₂ are PERPENDICULAR ifRead the answer and worked solution →The slope of the line joining (2, 3) and (5, 11) isRead the answer and worked solution →The slope-intercept form y = mx + c of the line 3x + 4y = 8 gives a slope ofRead the answer and worked solution →The equation of the line passing through (2, −1) with slope 3 isRead the answer and worked solution →Equation of the line passing through (3, 4) and parallel to the line 2x − 3y = 5 isRead the answer and worked solution →The distance from the point (0, 0) to the line 3x + 4y − 25 = 0 isRead the answer and worked solution →The angle θ between two lines with slopes m₁ and m₂ satisfiesRead the answer and worked solution →The distance between the parallel lines 3x + 4y = 7 and 3x + 4y = 12 isRead the answer and worked solution →The intercept form of the equation of a line making intercepts a and b on the x- and y-axes isRead the answer and worked solution →The line 3x − 4y + 12 = 0 cuts the y-axis atRead the answer and worked solution →
Worked practice questions
The x-intercept of the line $2x + 3y = 12$ is:
- 12
- 6
- $-6$
- 4
Show answer and solution
Correct answer: B. 6
Set y = 0: 2x = 12 ⟹ x = 6.
The slope of a line perpendicular to $y = 3x + 2$ is:
- $3$
- $\tfrac13$
- $-3$
- $-\tfrac13$
Show answer and solution
Correct answer: D. $-\tfrac13$
y = 3x+2 has slope 3; a perpendicular line has slope −1/3.
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