Condition for Two Lines to Be Parallel

Q. If two lines having slopes $m_1$ and $m_2$ are parallel to each other, then which of the following is correct?

1. $m_1=m_2$
2. $m_1\times m_2=1$
3. $\frac{m_1}{m_2}=2$
4. $m_1=3\times m_2$

Q.

A rectangle ABCD, A = (0, 0), B = (4, 0), C = (4, 2), D = (0, 2) undergoes the following transformations successively.
(i) $f_1(x,y)\to (y,x)$
(ii) $f_2(x,y)\to (x+3y,y)$
(iii) $f_3(x,y)\to (\frac{x-y}{2},\frac{x+y}{2})$
The final figure will be

1. a rhombus

2. a rectangle

3. a square

4. a parallelogram

Q.

If PS is the median of the triangle with vertices P(2, 2), Q(6, -1) and R(7, 3) then equation of the line passing through (1, -1) and parallel to PS is

1. $4x-7y-11=0$

2. $2x+9y+7=0$

3. $4x+7y+3=0$

4. $2x-9y-11=0$

Q.

Equation of a line which is parallel to the line common to the pair of lines given by $6x^2-xy-12y^2-0$ and $15x^2+14xy-8y^2-0$ and at a distance 7 from it is

1. $3x+4y=35$

2. $5x-2y=7$

3. $3x+4y=-35$

4. $2x-3y=7$

Q. Equation of the line passing through (1, 2) and parallel to the line $y=3x–1$ is

1. y + 2 = x + 1
2. y + 2 = 3(x + 1)
3. y – 2 = 3(x – 1)
4. y – 2 = x – 1

Q. If the line 2x+3y=5 and y=mx+c be parallel, then

1. $m=-\frac{2}{3},c$ = any real number
   
2. $m=\frac{2}{3},c=5$
3. $m=-\frac{2}{3},c=5$
4. None of these

Q.

A rectangle ABCD, A = (0, 0), B = (4, 0), C = (4, 2), D = (0, 2) undergoes the following transformations successively.
(i) $f_1(x,y)\to (y,x)$
(ii) $f_2(x,y)\to (x+3y,y)$
(iii) $f_3(x,y)\to (\frac{x-y}{2},\frac{x+y}{2})$
The final figure will be

1. a square

2. a rectangle

3. a parallelogram

4. a rhombus

Q. If two lines having slopes $m_1$ and $m_2$ are parallel to each other, then which of the following is correct?

1. $m_1\times m_2=1$
2. $m_1=m_2$
3. $\frac{m_1}{m_2}=2$
4. $m_1=3\times m_2$

Q. Equation of the line passing through (1, 2) and parallel to the line $y=3x–1$ is

1. y + 2 = x + 1
2. y + 2 = 3(x + 1)
3. y – 2 = 3(x – 1)
4. y – 2 = x – 1

Q. If the line 2x+3y=5 and y=mx+c be parallel, then

1. $m=\frac{2}{3},c=5$
2. None of these
3. $m=-\frac{2}{3},c=5$
4. $m=-\frac{2}{3},c$ = any real number