Two Point Form of a Straight Line

Q. Draw the graphs of following equations:

2x − y = 1 and x + 2y = 13

(i) find the solution of the equations from the graph.

(ii) shade the triangular region formed by the lines and the y-axis.

Q. Solve the following simultaneous equations graphically.
(1) x + y = 6 ; x – y = 4
(2) x + y = 5 ; x – y = 3
(3) x + y = 0 ; 2x – y = 9
(4) 3x – y = 2 ; 2x – y = 3
(5) 3x – 4y = –7 ; 5x – 2y = 0
(6) 2x – 3y = 4 ; 3y – x = 4

Q. If the points (−2, −1), (1, 0), (x, 3) and (1, y) form a parallelogram, find the values of x and y.

Q.

A (1, -5), B (2, 2) and C (-2, 4) are the vertices of triangle ABC. Find the equations of :

(i) the median of the triangle through A.

(ii) the altitude of the triangle through B.

(iii) the line through C and parallel to AB.

Q.

Find the equation of a line with x intercept = 5 and passing through the point (4, –7).

1. 7x – 35 = y

2. 6x – 24 = y

3. 7x – 42 = y

4. 2x – 56 = y

Q. If the coordinates of the mid-points of the sides of a triangle are (1, 1) (2, −3) and (3, 4), find the vertices of the triangle.

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:
$$\begin{gathered} x-y-5=0 \\ 3x+5y-15=0 \end{gathered}$$

Q.

Find the equation of the line with x-intercept 5 and a point on it (-3, 2).

Q. Solve the following system of equations graphically:

Q.

A straight line passes through the points P(-1, 4) and Q(5, -2). It intersects the co-ordinates axes at points A and B. M is the mid-point of the segment AB. Find :

(i) The equation of the line.

(ii) The co-ordinates of A and B.

(iii) The co-ordinates of M.

Q.

Find the point where 3x + 2y = 8 intersects the Y axis.

Q.

Find the equation of the line through (1, 3) and making an intercept of 5 on the y-axis.

Q.

If the coordinates of the vertices of the triangle $\mathrm{ABC}$ be $\left(-1,6\right),\left(-3,-9\right),$ and $\left(5,-8\right)$ respectively, then the equation of the median through $\mathrm{C}$ is:

1. $13x-14y-47=0$

2. $13x-14y+47=0$

3. $13x+14y+47=0$

4. $13x+14y-47=0$

Q.

The co-ordinates of two points A and B are (-3, 4) and (2, -1). Find :

(i) the equation of AB;

(ii) the co-ordinates of the point where the line AB intersects the y-axis.

Q. Complete the following table to draw graph of the equations–
(I) x + y = 3 (II) x – y = 4

x + y = 3 x 3 $\boxed{0}$ $\boxed{0}$ y $\boxed{0}$ 5 3 (x, y) (3, 0) $\boxed{0}$ (0, 3)

x – y = 4 x $\boxed{0}$ –1 0 y 0 $\boxed{0}$ –4 (x, y) $\boxed{0}$ $\boxed{0}$ (0, –4)

Q. If the coordinates of the mid-points of the sides of a triangle be (3, −2), (−3, 1) and (4, −3), then find the coordinates of its vertices.

Q. Find the equation of the line passing through the point (2, -5) and making an intercept of -3 on the Y axis.

Q.

In triangle ABC, the co-ordinates of vertices A, B and C are (4, 7), (-2, 3) and (0, 1) respectively. Find the equation of median through vertex A.

Also, find the equation of the line through vetex B and parallel to AC.

Q. Find the lengths of the medians of a ΔABC having vertices at A(5, 1), B(1, 5), and C(−3, −1).

Q. If A (−1, 3), B (1, −1) and C (5, 1) are the vertices of a triangle ABC, find the length of the median through A.

Q.

Find the equation of the line, whose :

(i) x-intercept = 5 and y-intercept = 3

(ii) x-intercept = -4 and y-intercept = 6

(iii) x-intercept = -8 and y-intercept = -4

Q. If the coordinates of the mid-points of the sides of a triangle are (3, 4) (4, 6) and (5, 7), find its vertices.

Q. If (−1, 2), (2, −1) and (3, 1) are any three vertices of a parallelogram, then

(a) a = 2, b = 0

(b) a= −2, b = 0

(c) a = −2, b = 6

(d) a = 6, b = 2

Q. Equation of a line through the origin and perpendicular to the line joining (a, 0) and (-a, 0), is

1. y = 0
2. x = 0
3. x = –a
4. y = ­–a

Q. At 4.30 pm, the equation of line along minute hand is ( x=0 ) . Therefore, a this instant, the equation of line along the hour hand will be. 1- x+y = 0 2- x-y = 0 3- y = root2 x 4- y = x/root2

Q.

Draw the graphs of the equations 5x - y = 5 and 3x - y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and y-axis. Calculate the area of the triangle so formed.

Q.

state the equation of the line which has the y-intercept -5 and is equally inclined to the axes.

Q.

Plot the points A (1, 1), B (4, 7) and C (4, 10) on a graph paper. Connect A and B, and also A and C.

Which segment appears to have the steeper slope, AB or AC?

Justify your conclusion by calculating the slopes of AB and AC.

Q.

Find the equation of the straight line passing through origin and the point of intersection of the lines x + 2y = 7 and x - y = 4.

Q.

P(3, 4), Q(7, -2) and R(-2, -1) are the vertices of triangle PQR. Write down the equation of the median of the triangle through R.

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

2. $x-7y-3=0$

3. $2x-7y-3=0$

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