Mathematics

Straight Lines and Coordinates

164 Questions

Straight lines and coordinates form the basis of coordinate geometry. This topic focuses on finding slopes, equations of lines, and points of intersection. These mathematical concepts are essential for performing well in advanced quantitative aptitude tests.

Line equations and slopesPoint of intersectionConcurrent linesNormal and parallel linesAngle between lines

Straight Lines and Coordinates Questions

Multiple choice maths average arithmetic mean of ap introduction to averages means

A line is such that the algebraic sum of the perpendicular on it from a number of point is zero. The line always passes through a fixed point that is 

  1. A. M of the given points

  2. GM of the given points

  3. HM of the given points

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The algebraic sum of perpendiculars from points (xi, yi) to a line ax + by + c = 0 being zero implies the line passes through the centroid (mean of x, mean of y).

Multiple choice maths arithmetic progressions complete the a.p series with given information properties of an ap problems on ap

A line passes through the variable point $A(\lambda +1,2\lambda)$ meets the lines $7x+y-16=0,\ 5x-y-8=0,\ x-5y+8=0$ at $b,c,d$ respectively. Then $AC, AB, AD$ are in

  1. A.P

  2. G.P

  3. H.P

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By calculating the distances from A to the lines, one can show that the segments form an arithmetic progression based on the properties of the lines and the point A.

Multiple choice

What is the equation of the line that passes through the points ((2, 3)) and ((5, 7))?

  1. \(y = 2x + 1\)
  2. \(y = 2x - 1\)
  3. \(y = x + 3\)
  4. \(y = x - 3\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation of a line that passes through two points ((x_1, y_1)) and ((x_2, y_2)) is given by the point-slope form: (y - y_1 = \frac{y_2 - y_1}{x_2 - x_1} (x - x_1)). Substituting the values of (x_1, y_1, x_2,) and (y_2) into the formula, we get: (y - 3 = \frac{7 - 3}{5 - 2} (x - 2)) = (y - 3 = \frac{4}{3} (x - 2)) = (y - 3 = \frac{4}{3}x - \frac{8}{3}) = (y = \frac{4}{3}x - \frac{8}{3} + 3) = (y = \frac{4}{3}x + 1). Therefore, the equation of the line that passes through the points ((2, 3)) and ((5, 7)) is (y = 2x + 1).

Multiple choice

What is the slope of the line passing through the points (1, 2) and (3, 4)?

  1. 1

  2. 2

  3. 3

  4. 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula (y2 - y1)/(x2 - x1). Substituting the given points, we get (4 - 2)/(3 - 1) = 2.

Multiple choice

What is the equation of the line passing through the point (2, 3) and having a slope of -2?

  1. y = -2x + 7

  2. y = -2x + 5

  3. y = -2x + 3

  4. y = -2x + 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation of a line passing through a point (x1, y1) and having a slope m is given by the formula y - y1 = m(x - x1). Substituting the given point and slope, we get y - 3 = -2(x - 2), which simplifies to y = -2x + 7.

Multiple choice

A line is a one-dimensional geometric figure that extends infinitely in both directions. What is the equation of a line that passes through the points (2, 3) and (5, 7)?

  1. y = 2x + 1

  2. y = 2x - 1

  3. y = x + 3

  4. y = x - 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The equation of a line that passes through the points (2, 3) and (5, 7) is y = 2x - 1.

Multiple choice

What is the equation of a line that passes through the points (2, 3) and (5, 7)?

  1. y = x + 1

  2. y = 2x + 1

  3. y = 3x - 1

  4. y = 4x + 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The equation of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula $y - y_1 = (y_2 - y_1)/(x_2 - x_1) * (x - x_1)$. Substituting the given values, we get $y - 3 = (7 - 3)/(5 - 2) * (x - 2)$. Simplifying, we get $y = 2x + 1$.

Multiple choice

What is the slope of the line represented by the equation 3x - 2y = 6?

  1. 3/2

  2. 2/3

  3. -3/2

  4. -2/3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The slope of a line in the form $Ax + By = C$ is given by the formula $m = -A/B$. Substituting the given values, we get $m = -3/-2 = 3/2$.

Multiple choice

What is the equation of a line that is perpendicular to the line y = 2x + 1 and passes through the point (3, 4)?

  1. y = -(1/2)x + 5

  2. y = -(1/2)x + 7

  3. y = (1/2)x + 5

  4. y = (1/2)x + 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The slope of the line y = 2x + 1 is 2. The slope of a line perpendicular to this line is the negative reciprocal of 2, which is -1/2. Using the point-slope form of a line, we can write the equation of the line as $y - 4 = (-1/2)(x - 3)$. Simplifying, we get $y = -(1/2)x + 7$.

Multiple choice

What is the equation of a line that passes through the points (2, 3) and (5, 7)?

  1. y = 2x + 1

  2. y = 2x - 1

  3. y = x + 3

  4. y = x - 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation of a line that passes through two points (x1, y1) and (x2, y2) is given by the formula y - y1 = (y2 - y1)/(x2 - x1) * (x - x1). Substituting the values of the two points, we get y - 3 = (7 - 3)/(5 - 2) * (x - 2). Simplifying this equation, we get y = 2x + 1.

Multiple choice

What is the equation of a line that passes through the points (2, 3) and (5, 7)?

  1. y = 2x + 1

  2. y = 2x - 1

  3. y = x + 3

  4. y = x - 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation of a line passing through two points (x1, y1) and (x2, y2) is given by the formula (y - y1) / (x - x1) = (y2 - y1) / (x2 - x1). Substituting the given points, we get (y - 3) / (x - 2) = (7 - 3) / (5 - 2) = 2. Solving for y, we get y = 2x + 1.

Multiple choice

What is the slope of the line that passes through the points (2, 3) and (5, 7)?

  1. 1

  2. 2

  3. 3

  4. 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The slope of a line is given by the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. In this case, (x1, y1) = (2, 3) and (x2, y2) = (5, 7), so the slope is (7 - 3) / (5 - 2) = 4 / 3 = 2.

Multiple choice

What is the equation of the line that passes through the point (3, 4) and has a slope of -2?

  1. y = -2x + 10

  2. y = -2x + 2

  3. y = -2x + 6

  4. y = -2x + 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation of a line in slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the slope is -2 and the y-intercept is 4, so the equation of the line is y = -2x + 4.

Multiple choice

What is the equation of a line that passes through the points (2, 3) and (5, 7)?

  1. y = 2x + 1

  2. y = 3x - 1

  3. y = 4x - 5

  4. y = 5x - 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation of a line that passes through two points (x1, y1) and (x2, y2) is given by the formula y - y1 = (y2 - y1)/(x2 - x1) * (x - x1). Substituting the values of the two points, we get y - 3 = (7 - 3)/(5 - 2) * (x - 2). Simplifying this equation, we get y = 2x + 1.

Multiple choice

What is the slope of the line that passes through the points (2, 3) and (5, 7)?

  1. 1

  2. 2

  3. 3

  4. 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The slope of a line is given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. Therefore, the slope of the line that passes through the points (2, 3) and (5, 7) is (7 - 3) / (5 - 2) = 4 / 3 = 2.