Coordinate Axes and Cartesian Plane

Q.

What is $y=mx+c$? Explain

Q.

The pair of equations $x=a$ and $y=b$ graphically represent lines which are,

1. Parallel

2. Intersecting at $(b,a)$

3. Coincident

4. Intersecting at $(a,b)$

Q.

Question 10
A point lies on positive direction of x-axis at a distance of 7 units from the y-axis. What are its Coordinates, if this lies in the negative direction of y-axis at a distance of 7 units from x-axis?

Q.

Statement-1: The coordinate of a point on the x-axis is of the form (x, 0) and that of the point on the y-axis is (y, 0).
Statement-2: The point of intersection of the axes is called the origin.
Which of the following is true?

1. Statement 1 is false and Statement 2 is true.

2. Statement 1 is true and Statement 2 is false.

3. Both the Statement 1 and 2 are true.

4. Both the Statement 1 and 2 are false.

Q.

Find the area of a curve $xy=4$ bounded by the lines $x=1$ and $x=3$ and $x-axis$

1. $\cos \left(12\right)$

2. $\log \left(64\right)$

3. $\log \left(81\right)$

4. $\log \left(27\right)$

Q.

Given the point P (3, 4). What is the distance of point P from (a) x-axis (b) y-axis?

Q.

The equation of the y - axis is

(a) x = 0

(b) y = 0

(c) x = y

(d) x + y = 0

Q.

Any point on the y - axis is of the form

(a) (x, y)

(b) (0, y)

(c) (x, 0)

(d) (y, y)

Q.

Assertion: The coordinates of the origin are (0, 0).
Reason: Origin has zero distance from both the x-axis and y-axis.
Which of the following is correct?

1. Both A and R are true and R is not the correct explanation of A.

2. A is false and R is true.

3. Both A and R are true and R is the correct explanation of A.

4. A is true and R is false.

Q.

The equation of the x - axis is

(a) x = 0

(b) y = 0

(c) x = y

(d) x + y = 0

Q. A point lies on. x axis at a distance of 9 units from y axis what are its coordinates

Q.

Describe Graphing Linear Equations

Q.

Any point on the x - axis is of the form

(a) (x, y)

(b) (0, y)

(c) (x, 0)

(d) (x, x)

Q.

Draw a line parallel to the x-axis at a distance of 2 units below the x-axis. [2 MARKS]

Q.

The line represented by the equation x = a is perpendicular to ____.

1. x-axis

2. y-axis

3. the line x = 4

4. the line x = -2

Q. Which of the following statements is not always correct?

1. x – 3 = 0, is the equation of a line parallel to the y-axis and passing through (3, 0).
2. The equation y = 4x + 3b, where b is a constant, has infinitely many solutions.
3. The equation of line whose x-coordinate is always thrice of the y-coordinate is x = 3y.
4. The graph of the equation y = mx + c always passes through the origin.

Q.

The equation of y-axis is:

1. x = 0

2. x + y = 0

3. y = 0

4. x = y

Q.

Write the equation of y -axis in term of x and y

Q. Draw the graph of the equation, y = −x.

Q. In point B(5, 6), 6 is called .

1. Abscissa
2. Ordinate
3. Origin

Q.

Give the geometric representation of y = 3 as an equation

(I) in one variable

(II) in two variables

Q. y = 0 is the equation of
(a) the x-axis
(b) the y-axis
(c) a line parallel to the x-axis
(d) a line parallel to the y-axis

Q.

How many linear equation in $x$ and $y$ can be satisfied by $x=2$ and $y=3$ ?

1. Only one

2. Only two

3. Infinite

4. Zero

Q. A line passes through the point (-4, 6) and is parallel to x-axis. Find its equation.

Q. If $3x–4y+12=0$ and $3x+2y–6=0$, then area of triangle formed by the given lines and x-axis is (in sq. units)

1. 8
2. 9
3. 11
4. 12

Q.

Lines perpendicular to the X axis are represented by the equation x = a

1. True

2. False

Q. Write the equation of straight line passing through the points (-1, 1), (0, 0) and (1, -1)

Q. The co-ordinate is the perpendicular distance of the point from the x-axis.

1. x
2. y
3. z

Q.

Coordinates of a point on the y-axis is of the form _____________.
[2 MARKS]

Q.

Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.

$\begin{array}{ccccc}x& -2& -1& 0& 3\\ y& 8& 7& -1.25& -1\end{array}$