Slope of a Line

Q.

If two lines are perpendicular, then the product of their slope is _____.

1. 0

2. 1

3. -1

4. infinite

Q. In which ratio is the line segment joining points (-3, -4) and (1, -2) divided by y - axis

Q. Draw the graph of the lines x = $-$2 and y = 3 . Write the vertices of the figure formed by these lines , the x-axis and the y-axis . Also , find the area of the figure.

Q. Draw the graphs of the following equations on the same graph paper:
$$\begin{gathered} 2x+y=2 \\ 2x+y=6 \end{gathered}$$
Find the coordinates of the vertices of the trapezium formed by these lines. Also, find the area of the trapezium so formed.

Q. The product of slopes of two perpendicular lines is ___ .

Q.

Find the slope, x-intercept & y-intercept of the straight line 2x - 3y + 5 = 0.

Q. The line segment joining the points P(3, 3) and Q(6, −6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.

Q.

A (1, 4), B (3, 2) and C (7, 5) are vertices of a triangle ABC. Find :

(i) the co-ordinates of the centroid of triangle ABC.

(ii) the equation of a line, through the centroid and parallel to AB.

Q. Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.

Q. What is wavy curve method .? What are the steps to solve inequality by wavy curve method?

Q. What is the slope of a line segment whose inclination is ${135}^{\circ }$?

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

Q.

The line joining $P(-4,5)$ and $Q(3,2)$ intersect the $y$-axis at point $R$ .$PM$ and $QN$ are perpendicular to $P$ and $Q$ on the $x$- axis. Find:

(1) the ratio $PR:RQ$.

(2) the coordinate of $R$.

(3) the area of the quadrilateral $PMNQ$.

Q.

Find the slope, x-intercept & y-intercept of the straight line 2x - 3y + 5 = 0.

Q.

The number of integral values of $m$ so that the abscissa of point of intersection of lines $3x+4y=9$ and $y=mx+1$ is also an integer, is:

1. $3$

2. $2$

3. $1$

4. $0$

Q.

In fig., OP is equal to diameter of the circle. Prove that ΔABP is an equilateral triangle.

Q. Find the slope of the line passing through the points A(4, -1) and B(-3, 5).

1. $\frac{-7}{6}$
2. $\frac{-6}{7}$
3. $\frac{6}{7}$
4. $\frac{7}{6}$

Q.

If a line passes through the point (1, 2) and cuts off positive intercepts on the x–axis and y–axis in the ratio 2 : 3, find the equation of the line.

1. 7 = 3x + 2y

2. 5= 3x + 8y

3. 4 = 3x + 2y

4. 3 = 2x + 7y

Q.

A line through the point $A(2,0)$ which makes an angle of $30°$with the positive direction of X-axis is rotated about$A$ in clockwise direction through an angle of $15°$ . Then, the equation of the straight line in the new position is

1. $(2–\sqrt{3})x+y+4-2\sqrt{3}=0$

2. $(2–\sqrt{3})x–y–4+2\sqrt{3}=0$

3. $(2–\sqrt{3})x+y-4-2\sqrt{3}=0$

4. $(2–\sqrt{3})x+y+4+2\sqrt{3}=0$

Q.

Inclination of a line parallel to x axis is _____.

1. 0 degree

2. 90 degree

3. 80 degree

4. 40 degree

Q. What is a slope?

Q.

The co-ordinates of two points P and Q are (2, 6) and (-3, 5) respectively. Find :

(i) the gradient of PQ;

(ii) the equation of PQ;

(iii) the co-ordinates of the point where PQ intersects the x-axis.

Q.

The line joining the points $(-1,3)$and $(4,-2)$ will pass through the point $(p,q)$if

1. $p–q=1$

2. $p+q=1$

3. $p–q=2$

4. $p+q=2$

Q. If (−2, 1) is the centroid of the triangle having its vertices at (x , 0) (5, −2), (−8, y), then x, y satisfy the relation

(a) 3x + 8y = 0

(b) 3x − 8y = 0

(c) 8x + 3y = 0

(d) 8x = 3y

Q. Determine whether the given points are collinear.
(1) A(0, 2), B(1, –0.5), C(2, –3)

(2) $\mathrm{P}\left(1,2\right),\mathrm{Q}\left(2,\frac{8}{5}\right),\mathrm{R}\left(3,\frac{6}{5}\right)$

(3) L(1, 2), M(5, 3) , N(8, 6)

Q.

A and B are two points on the x-axis and y-axis respectively. P(2, -3) is the mid point of AB. Find the

(i) co-ordinates of A and B

(ii) slope of line AB

(iii) equation of line AB.

Q. The line joining the points (2, 1) and (5, −8) is trisected at the points P and Q. If point P lies on the line 2x − y + k = 0. Find the value of k.

Q.

Find the equation of the line whose slope is $-\frac{5}{6}$ and x-intercept is 6.

Q. If the slope of the line joining the points P(k, 0) and Q(-3, -2) is $\frac{2}{7}$, then k = ______________.

1. 1
2. 2
3. 3
4. 4

Q. Solve the following system of equations graphically and find the vertices and area of the triangle formed by these lines and the y-axis.
$$\begin{gathered} 2x-5y+4=0 \\ 2x+y-8=0 \end{gathered}$$

Q.

The side AB square ABCD is parallel to the x-axis. Find the slopes of all its sides.

Also, find :

(i) the slope of the diagonal AC,

(ii) the slope of the diagonal BD.