Mathematics

Straight Lines and Coordinates

155 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

What is the equation of a line in three-dimensional space?

  1. $x = A + Bt$, $y = C + Dt$
  2. $x = A + Bt$, $y = C + Dt$, $z = E + Ft$
  3. $x = A + Bt + Ct^2$, $y = C + Dt + Et^2$
  4. $x = A + Bt$, $y = C + Dt$, $z = E + Ft + Gt^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The equation of a line in three-dimensional space is given by $x = A + Bt$, $y = C + Dt$, $z = E + Ft$, where A, B, C, D, E, and F are constants.

Multiple choice

What is the equation of the line that passes through the two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$?

  1. $x = A + Bt$, $y = C + Dt$
  2. $x = A + Bt$, $y = C + Dt$, $z = E + Ft$
  3. $x = A + Bt + Ct^2$, $y = C + Dt + Et^2$
  4. $x = A + Bt$, $y = C + Dt$, $z = E + Ft + Gt^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The equation of the line that passes through the two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is given by $x = A + Bt$, $y = C + Dt$, $z = E + Ft$, where A, B, C, D, E, and F are constants.

Multiple choice

Find the equation of the line that passes through the points $(2, 3)$ and $(5, 7)$.

  1. $y = x + 1$
  2. $y = 2x - 1$
  3. $y = 3x - 2$
  4. $y = 4x - 3$
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 $y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$. Substituting the given points, we get $y - 3 = \frac{7 - 3}{5 - 2}(x - 2) = \frac{4}{3}(x - 2)$. Simplifying, we get $y - 3 = \frac{4}{3}x - \frac{8}{3} = \frac{4}{3}x - \frac{24}{9} = \frac{4}{3}x - 8$. Therefore, the equation of the line is $y = \frac{4}{3}x - 8 + 3 = \frac{4}{3}x - 5$.

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 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

Find the slope of the line passing 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 passing through two points $$ (x_1, y_1) $$ and $$ (x_2, y_2) $$ is given by the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Substituting the given points, we get: $$m = \frac{7 - 3}{5 - 2}$$ $$m = \frac{4}{3}$$