Intercept of a Straight Line

Q. Find the equation of a straight line which cuts off an intercept of length 3 on y - axis and is parallel to the line joining the points (3, -2) and (1, 4).

1. 3x + 2y - 3 = 0
2. 3x + y - 3 = 0
3. 3x + y - 1 = 0
4. 3x + y - 7 = 0

Q.

A line y = mx (where m is the slope) will always pass through the point

1. (0, 0)

2. (0, 1)
3. (1, 0)
4. (1, 1)

Q.

The equation of a straight line which passes through the point (3, 4) and whose intercept on y-axis is twice that of x-axis, is

1. 2x + y = 10

2. x + 2y = 10

3. 2x – y = 10

4. 3x-4y+7=0

Q.

Question 6
The vertices of triangle ABC are A (4, 6), B (1, 5) and C (7, 2). A line is drawn to intersect sides AB and AC at D and E respectively, such that $\frac{AD}{AB}=\frac{AE}{AC}=\frac{1}{4}$. Calculate the area of triangle ADE and compare it with area of triangle ABC.

Q.

Find the equation of the line which passes through the point (3, 4) and the sum of its intercepts on the axes is 14.

1. $2x+y-7=0$

2. $x+y-7=0$

3. $x-y-7=0$

4. $x+y+7=0$

Q. Find the equation of a line that has y-intercept 4 and is perpendicular to line joining (2, -3) and (4, 2).

1. 2x + 5y - 19 = 0
2. 2x + 5y - 20 = 0
3. 2x + 4y - 20 = 0
4. 5x + 2y - 20 = 0

Q.

Solve the following system of equations graphically. Determine the vertices of the triangle formed by the lines and the given axis.

$4x-5y-20=0;3x+5y-15=0,y-axis$

Q.

The points A(-a, b), B(-a, c) and C(a, c) form the vertices of a triangle. Which of the following is true?

1. $\Delta ABC$ is a right angled triangle, right angled at A.
2. Area of the triangle = b(a - c)
3. The triangle is equilateral.
4. Area of the triangle = a(c - b)

Q.

1. Both $A$ and $R$ are true and $R$ is the correct explanation of $A$ .
2. Both A and $R$ are true and $R$ is not the correct explanation of $A$ .
3. $A$ is true but $R$ is false .
4. $A$ is false but $R$ is true .

Q.

The equation of the straight line making an intercept of 3 units on the y-axis and inclined at ${45}^{\circ }$ to the x-axis is

1. y=x-1

2. y = x + 3

3. y = 45x + 3

4. y = x + 45

Q. Find the coordinates of the points where the graph of line $3x+2y=6$ drawn meets the co-ordinate axes?

1. x-axis at $(a,0)=(-2,0)$; y-axis at $(0,b)=(0,-3)$
2. x-axis at $(a,0)=(2,0)$; y-axis at $(0,b)=(0,3)$
3. x-axis at $(a,0)=(-2,0)$; y-axis at $(0,b)=(0,3)$
4. x-axis at $(a,0)=(2,0)$; y-axis at $(0,b)=(0,-3)$

Q. Which of the following represents the equation of the line making an intercept of 3 unit with the positive x-axis and passing through the point (2, 1)?

1. y - x - 3 = 0
2. y - x + 3 = 0
3. y + x - 3 = 0
4. y + x + 3 = 0

Q. The line joining two points $A(2,0)$ and $B(3,1)$ ir rotated about $A$ about in the anticlock wise direction through an angle of ${15}^o$. The equation of the line in the new position is:

1. $x-\sqrt{3}y-2=0$
2. $x-2y-2=0$
3. $\sqrt{3}x-y-2\sqrt{3}=0$
4. $\sqrt{2}x-y-2\sqrt{2}=0$

Q. Find the area of a rhombus if its vertices are $\left(3,0\right),\left(4,5\right),\left(-1,4\right)and\left(-2,-1\right)$ taken in order.

Q. The equation of a line AB is 2x - 2y + 3 = 0. The x-intercept of the line AB is:

1. 3
2. 2
3. -1.5
4. 1

Q. If the lines given by 3x + 2ky = 2 and 2x + 5y = 1 are parallel, then the value of 'k' is.

1. $\frac{15}{4}$
2. $\frac{4}{3}$
3. $\frac{3}{4}$
4. $\frac{4}{15}$

Q. The line joining two points $A(2,0);B(3,1)$ is rotated about $A$ in the anticlockwise direction through an angle of ${15}^o$. The equation of the line in the new position is :

1. $x-\sqrt{3y}-2=0$
2. $x-2y-2=0$
3. $\sqrt{3x}-y-2\sqrt{3}=0$
4. none

Q.

Find the equation of the line through $(-2,3)$ with slope $-4$

1. 2x + y + 5 = 0

2. 4x + y + 1 = 0

3. 4x - y + 5 = 0

4. 4x +y + 5 = 0

Q. Find the equation of the line passing through the point $(2,3)$ and making intercept of length $2$ units between the lines $y+2x=3$ and $y+2x=5$

1. $x=2$
2. $x-4y=18$
3. $3x+4y=18$
4. $x+2=0$

Q. The line joining two points $A(2,0),B(3,1)$ is rotated about $A$ in anti-clockwise direction through an angle of ${15}^{\circ }$. The equation of the line in the now position, is

1. $\sqrt{3}x-y-2\sqrt{3}=0$
2. $x-3\sqrt{y}-2=0$
3. $\sqrt{3}x+y-2\sqrt{3}=0$
4. $x+\sqrt{3}y-2=0$

Q. Find the equation of the straight line that has a $y-$intercept of 5 and is parallel to the straight line $x-3y=3.$

1. $x-3y+15=0$
2. $x+3y+5=0$
3. $x+3y-5=0$
4. $x-3y-5=0$

Q. The equation Of the line passing through (1, 5) and making an angle ${135}^{\circ }$ with the x-axis is

1. x-y+4=0
2. x-y-4=0
3. x+y-2=0
4. x+y-6=0

Q. Find the equation of the line passing through the point of intersection of the lines $3x-4y+1=0$ and $5x+y-1=0$ and cutting off equal intercepts from the axes.

Q. The equation of a straight line which makes an angle ${45}^o$ with the x-axis with y-intercept $101$ units is:

1. $101x+y=1$
2. $x-y+101=0$
3. $10x+101y=1$
4. $x+y-101=0$

Q. The equation of straight passes through the point (-3, 5) such that the portion of it between the axes is divided by the the ratio 5:3 internally (reckoning from x-axis ) will be -

1. x + y+z = 0
2. 2x + y +1 = 0
3. x + 2 y - 7 = 0
4. x - y+8 =0

Q. Find the equation of line passing through the point (1, -1) and making an angle ${45}^o$ with the positive direction of x-axis.

Q. In what ratio is the line joining the points $(-5,1)$ and $(2,3)$ divided by the y-axis? Also, find the point of intersection.

1. $5:2$ internally, $(0,\frac{17}{7})$
2. $5:2$ internally, $(0,\frac{12}{7})$
3. $5:2$ internally, $(0,\frac{17}{5})$
4. None of these

Q. Find the equation of a line whose inclination is ${30}^{\circ }$ and making an intercept of -3/5 on the y-axis

1. $y=\frac{5}{\sqrt{6}}x+\frac{2}{5}$
2. $y=\frac{1}{\sqrt{3}}x-\frac{3}{5}$
3. $\frac{-5}{3}x$
4. $y=\frac{3}{\sqrt{7}}x-\frac{1}{3}$

Q. Find the equation of the line through $(2,3)$ and making an angle ${30}^{\circ }$ with the y-axis

Q. What is the equation of the straight line cutting off an intercept $2$ from the negative direction of y-axis and inclined at ${30}^o$ with the positive direction of x-axis?

1. $x-\sqrt{3}y-2\sqrt{3}=0$
2. $x+2\sqrt{3}y-3\sqrt{2}=0$
3. $x-2\sqrt{3}y+3\sqrt{2}=0$
4. $x-2\sqrt{3}y-2\sqrt{3}=0$