General Form of a Straight Line

Q.

If the points (k, 2-2k), (1-k, 2k) and (-k-4, 6-2k) are collinear, the possible values of k are ..............

1. 

2. 1/2

3. 1

4. -1

Q.

Find the relation between p and q if n=3 , y=1 is a solution of a pair of lines x-4y+p=0 and 2x+y-q-2=0

Q.

Equations of lines which pass through the points of intersection of the lines $4x-3y-1=0$ and $2x-5y+3=0$ and are equally inclined to the axes are

1. $y\pm x=0$

2. $y–1=\pm 1(x–1)$

3. $x–1=\pm 2(y–1)$

4. None of these

Q.

The equations of the lines which cuts off an intercept -$1$ from $y$-axis and equally inclined to the axes are

1. $x-y+1=0,x+y+1=0$

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

3. $x-y-1=0,x+y+1=0$

4. None of the above

Q.

If the point (2k – 3, k + 2) lies on the line 2x + 3y + 15 = 0, find the value of k.

1. $k=\frac{-15}{7}$

2. $k=\frac{-13}{7}$

3. $k=\frac{15}{7}$

4. $k=\frac{13}{7}$

Q. The midpoint P of the line segment joining the points A(−10, 4) and B(−2, 0) lies on the line segment joining the points C(−9, −4) and D(−4, y). Find the ratio in which P divides CD. Also find the value of y.

Q.

Find the point of intersection of the lines 4x + 3y = 1 and 3x - y + 9 = 0. If this point lies on the line (2k - 1) x - 2y = 4; find the value of k.

Q. Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.

Q.

What is the equation of the line $x-3y=18$ in slope-intercept form?

Q. Consider the lines given by
$L_1:x+3y-5=0$
$L_2:3x-ky-1=0$
$L_3:5x+2y-12=0$

Match the Statements/Exp[ressions in Column I with the Statements/Expressions in Column II.

Column I	Column II
$L_1,L_2,L_3$ are concurrent, if	k = -9
$Oneof{L}_1,L_2,L_3$ is parallel to at least one of the other two, if	$k=\frac{6}{5}$
$L_1,L_2,L_3$ form a triangle, if	$k=\frac{5}{6}$
$L_1,L_2,L_3$ do not form a triangle, if	k = 5

1. none of these
2. (a) $\to$ (s), (b) $\to$ (p, q), (c) $\to$ (r), (d) $\to$ (p, q, s)
3. (a) $\to$ (p), (b) $\to$ (p, q, s), (c) $\to$ (r), (d) $\to$ (p, q)
4. (a) $\to$ (s), (b) $\to$ (p, q, s), (c) $\to$ (s, r), (d) $\to$ (p, q, s)

Q.

(i) The point (-3, 2) lies on the line ax + 3y + y = 0, calculate the value of a.

(ii) The line y = mx + 8 contains the point (-4, 4), calculate the value of m.

Q. If the point $P\left(\frac{1}{2},y\right)$ lies on the line segment joining the points A(3, −5) and B(−7, 9) then find the
ratio in which P divides AB. Also, find the value of y.

Q. If x=a, and y=b is the solution of the equation 2x+y=3 and x-y=3. Find the values of a and b.
​​​​​

Q.

In the equation 2x+3y =6, if x=3, find the value of y

___

Q.

If the points (1, -1), (2, 1) and (4, x) lie on a line, then x is __

Q. Find the condition that the point P(x, y) may lie on the line joining (3, 4) and (-5, -6).

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

Q.

If the slope of the line passing through the point $A(3,2)$ is $\frac{3}{4}$, then the point on the line $5$ units away from $A$is.

1. $(-1.-1)$

2. $(7,5)$

3. $(7,-5)$

4. Both A and B

Q.

Find the slope and y-intercept of the line :

(i) y = 4 (ii) ax - by = 0

(iii) 3x - 4y = 5

Q.

Find the value of k if the point (2, k) lies on the line 2x - y = 3

1. 0

2. 2

3. 1

4. 3

Q.

How to draw a graph of polynomial x cube - 4 x

Q. The point A divides the join of P (−5, 1) and Q(3, 5) in the ratio k:1. Find the two values of k for which the area of ΔABC where B is (1, 5) and C(7, −2) is equal to 2 units.

Q. Find the ratio in which the line segment joining the points A (3, -6) and B (5, 3) is divided by x-axis. Also find the co-ordinates of the point of intersection.

Q. Determine the ratio in which line 3x+y-9=0 divides the line segment joining the points (1, 3) and (2, 7)

Q.

The following figure shows a parallelogram ABCD whose side AB is parallel to the x-axis, $\angle$A = ${60}^{\circ }$ and vertex C = (7, 5). Find the equation of BC and CD.

Q. if the middle points of sides of a triangle abc is (2, 4), (4, 12), (8, 20) respectively then find A, B, C

Q.

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

(i) Find the slope of the line AB.

(ii) Calculate the angle that the line AB makes with the positive direction of the x-axis.

Q. If the point $C\left(-1,2\right)$ divides internally the line segment joining the points A (2, 5) and B( x, y ) in the ratio 3 : 4 , find the value of x² + y² .

Q. Question 1
Write whether the following statement is True or False?
The point (0, 3) lies on the graph of the linear equation 3x + 4y = 12.

Q. In what ratio does the origin divide the line segment joining points (-5, 0) and (10, 0)?

1. 1:2
2. 2:3
3. 5:3
4. 4:7

Q. In each of the figures given below, an altitude is drawn to the hypotenuse by a right-angled triangle. The length of different line-segment are marked in each figure. Determine x, y, z in each case.

(i)

(ii)