Sample QuestionsStraight Lines questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Two lines are said to be perpendicular if the product of their slope is equal to:
- ✓
$-1$
- B
$0$
- C
$1$
- D
$\frac{1}{2}$
Answer: A.
View full solution →If slope of a line is $4$ and $y-$intercept made by the line is $2$ then the equation of line will be:
- A
$y = 4x - 2$
- ✓
$y = 4x + 2$
- C
$y = 2x + 4$
- D
$y = 2x - 4$
Answer: B.
View full solution →Given the three straight lines with equations $5x + 4y = 0, x + 2y - 10 = 0$ and $2x + y + 5 = 0,$ then these lines are:
- A
- B
The sides of a right angled triangle
- ✓
- D
The sides of an equilateral triangle
Answer: C.
View full solution →Choose the correct answer.
A point equidistant from the lines $4x + 3y + 10 = 0, 5x – 12y + 26 = 0$ and $7x + 24y – 50 = 0$ is:
- A
$(1, -1)$
- B
$(1, 1)$
- ✓
$(0, 0)$
- D
$(0, 1)$
Answer: C.
View full solution →Find the equation of line parallel to $4x + y = 2$ and pass through $(2, 5):$
- ✓
$4x + y - 13 = 0$
- B
$4x + y + 13 = 0$
- C
$4x - y - 13 = 0$
- D
$4x - y + 13 = 0$
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$ Area of the triangle whose vertices are $(4, 4), (3, -2)$ and $(- 3, 16),$ is
Reason $(R)$ Area of triangle whose vertices are $(x_1, y_1), (x_2, y_2)$ and $(x_3, y_3),$ is $\frac{1}{2}\text{x}_1(\text{y}_2-\text{y}_3)+\text{x}_2(\text{y}_3-\text{y}_1)+\text{x}_3(\text{y}_1-\text{y}_2)$
- ✓
$A$ is true, $R$ is true; $R$ is acorrect explanation of $A$.
- B
$A$ is true, $R$ is true; $R$ is not a correct explanation of $A.$
- C
$A$ is true; $R$ is false
- D
$A$ is false; $R$ is true.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason(s) $(R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$ The distance between the lines $4x + 3y = 11$ and $8x + 6y = 15$ is $\frac{7}{10}$
Reason $(R)$ The distance between lines the $ax + by = c_1 $ and $ax + by = c_2 $ is given by $\frac{\text{c}_1-\text{c}_2}{\sqrt{\text{a}^2+\text{b}^2}}$
- ✓
$A$ is true, $R$ is true; $R$ is acorrect explanation of $A.$
- B
$A$ is true, $R$ is true; $R$ is not a correct explanation of $A.$
- C
$A$ is true; $R$ is false
- D
$A$ is false; $R$ is true.
Answer: A.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$ Slope of line $3x - 4y +10 = 0$ is $\frac{3}{4}$
Reason $(R) x -$ intercept and $y-$intercept of $3x - 4y + 10 = 0$ respectively are $\frac{-10}{3} $ and $\frac{5}{2}.$
- A
$A$ is true, $R$ is true; $R$ is acorrect explanation of $A.$
- ✓
$A$ is true, $R$ is true; $R$ is not a correct explanation of $A.$
- C
$A$ is true; $R$ is false
- D
$A$ is false; $R$ is true.
Answer: B.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$ The slope of the line $x +7y = 0$ is $\frac{1}{7}$ and $y -$ intercept is $0.$
Reason $(R)$ The slope of the line ; $6x + 3y - 5 = 0$ is $- 2$ and $y -$ intercept is $\frac{5}{3}.$
- A
$A$ is true, $R$ is true; $R$ is acorrect explanation of $A.$
- B
$A$ is true, $R$ is true; $R$ is not a correct explanation of $A.$
- C
$A$ is true; $R$ is false
- ✓
$A$ is false; $R$ is true.
Answer: D.
View full solution →Directions: In the following questions, the Assertions $(A)$ and Reason$(s) (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$ slope of line $3x - 4y + 10 = 0$ is $\frac{3}{4}.$
Reason $(R)\ x -$ intercept and $y-$ intercept of $3x - 4y + 10 = 0$ respectively are $\frac{-10}{3}$ and $\frac{5}{2}.$
- A
Both assertion and reason are true and reason is the correct explanation of assertion.
- ✓
Both assertion and reason are true but reason is not the correct explanation of assertion.
- C
Assertion is true but reason is false.
- D
Assertion is false but reason is true
Answer: B.
View full solution →State whether the statements:
The straight line 5x + 4y = 0 passes through the point of intersection of the straight lines x + 2y - 10 = 0 and 2x + y + 5 = 0.
State whether the statements:
The line $\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{b}}=1$ moves in such a way that $\frac{1}{\text{a}^2}+\frac{1}{\text{b}^2}=\frac{1}{\text{c}^2},$ where c is a constant. The locus of the foot of the perpendicular from the origin on the given line is $x^2 + y^2 = c^2.$
View full solution →State whether the statements:
Line joining the points (3, -4) and (-2, 6) is perpendicular to the line joining the points (-3, 6) and (9, -18).
State whether the statements:
The vertex of an equilateral triangle is (2, 3) and the equation of the opposite side is x + y = 2. Then the other two sides are $\text{y}-3=(2\pm\sqrt{3})(\text{x}-2).$
View full solution →State whether the statements:
The points A (-2, 1), B (0, 5), C (-1, 2) are collinear.
Find the values of $k$ for which the line $(k - 3) x - (4 - k^2)y + k^2 - 7k + 6 = 0$ is passing through the origin.
View full solution →Find the values of $k$ for which the line $(k–3) x – (4 – k^2 ) y + k^2 –7k + 6 = 0$ is parallel to the y-axis.
View full solution →Find the values of $k$ for which the line $(k–3) x – (4 – k^2 ) y + k^2 –7k + 6 = 0$ is parallel to the x-axis.
View full solution →Find the equation of the line parallel to the line $3x - 4y + 2 = 0$ and passing through the point $(–2, 3).$
View full solution →Reduce the equation into slope-intercept form and find the slope and the y-intercept.
y = 0
Find the value of p so that three lines 3x + y - 2 = 0, px + 2y - 3 = 0 and 2x - y - 3 = 0 may intersect at one point.
Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines x - 7y + 5 = 0 and 3x + y = 0
What are the points on the y-axis whose distance from the line $\frac{x}{3} + \frac{y}{4} = 1$ is 4 units.
View full solution →Find the values of $\theta $ and p, if the equation $x\cos \theta + y\sin \theta = p$ is the normal form of the line $\sqrt 3 x + y + 2 = 0$
View full solution →Find the angles between the lines $\sqrt 3 x + y = 1$ and $x + \sqrt 3 y = 1$
View full solution →Find the equation of a line drawn perpendicular to the line $\frac{x}{4}+\frac{y}{6}=1$ through the point where it meets the Y-axis.
View full solution →Find the perpendicular distance from the origin of the line joining the points $(\cos \theta ,\sin \theta )$ and $(\cos \phi ,\sin \phi )$.
View full solution →Find the equations of the lines which cut-off intercepts on the axes whose sum and product are $1$ and $-6$ respectively.
View full solution →A person standing at the junction (crossing) of two straight paths represented by the equations 2x - 3y + 4 = 0 and 3x + 4y - 5 = 0 wants to reach the path whose equation is 6x - 7y + 8 = 0 in the least time. Find equation of the path that he should follow.
Prove that the product of the lengths of the perpendiculars drawn from the points $\left( {\sqrt {{a^2} - {b^2}} ,0} \right)$ and $\left( { - \sqrt {{a^2} - {b^2}} ,0} \right)$ to the line $\frac{x}{a}\cos \theta + \frac{y}{b}\sin \theta = 1$ is $b^2.$
View full solution →Fill in the blank:
The line which cuts off equal intercept from the axes and pass through the point (1, -2) is ____.
Fill in the blank:
If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through ____.
Fill in the blank:
Equations of the lines through the point (3, 2) and making an angle of 45° with the line x - 2y = 3 are ____.
Fill in the blank:
A point moves so that square of its distance from the point (3, -2) is numerically equal to its distance from the line $5x - 12y = 3.$ The equation of its locus is ____.
View full solution →Fill in the blank:
The points (3, 4) and (2, -6) are situated on the ____ of the line 3x - 4y - 8 = 0.
Find the area of the triangle formed by the lines $y - x = 0, x + y = 0$ and $x - k = 0.$
View full solution →Find the direction in which a straight line must be drawn through the point $(-1, 2)$ so that its point of intersection with the line $x + y = 4$ may be at a distance of $3$ units from this point.
View full solution →Show that the equation of the line passing through the origin and making an angle $\theta$ with the line $y = mx + c$ is $\frac{y}{x} = \frac{{m \pm \tan \theta }}{{1 \mp m\tan \theta }}$.
View full solution →Find the equation of the line passing through the point of intersection of the lines 4x + 7y - 3 = 0 and 2x - 3y + 1 = 0 that has equal intercepts on the axis.
In the triangle ABC with vertices A(2, 3), B (4, -1) and C (1, 2) find the equation and length of altitude from the vertex A.