M.C.Q

Question 11 Mark

Write the correct answer in the following:
The point at which the two coordinate axes meet is called the:

Answer

Origin.
Solution:
The points at which the two coordinate axes meet is called the origin.

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Question 21 Mark

Point (-3, 5) lies in the:

Answer

Second quadrant.
Solution:
In point (-3, 5), x-coordinate is negative and y-coordinate is positive. So, the point lies in the second quadrant.

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Question 31 Mark

The point which lies on the y-axis at a distance of 5 units in the negative direction of the y-axis is:

Answer

(0, -5)
Solution:
The point which lies on the y-axis at a distance of 5 units in the negative direction of the y-axis is (0, -5).

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Question 41 Mark

Abscissa of a point is positive in:

Answer

Quadrant I and IV
Solution:
Abscissa means x-corrdinate.
In quadrant I and IV, the value of x is positive.
Thus, the abscissa of a point is positive in quadrant I and IV.

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Question 51 Mark

A symbol having a fixed value is called a ______.

Answer

Constant.
Solution:
A symbol having a fixed value is called a constant.
Any natural number, whole number, integers, rational number. A symbol having the variable values is called variable.

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Question 61 Mark

A point whose abscissa is -3 and ordinate 2 lies in:

Answer

Second quadrant.
Solution:
As we know that abscissa is negative in second and third coordinate and ordinate is positive in first and second coordinate. Therefore the given point (-3, 2) lies in second coordinate.

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Question 71 Mark

The area of $\triangle\text{AOB}$ having vertices A(0, 6), O(0, 0) and B(6, 0) is:

Answer

18sq units.
Solution:

Clearly, $\triangle\text{AOB}$ is a right-angled triangle.
$\therefore$ Area of $\triangle\text{AOB}=\frac{1}{2}\times\text{Base}\times\text{Height}$
$=\frac{1}{2}\times\text{OB}\times\text{OA}$
$=\frac{1}{2}\times6\times6$
= 18 square units.

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Question 81 Mark

The ordinate of any point on x-axis is:

Answer

0
Solution:
On X-axis, all points have their Y-intercept = 0
So their ordinate = 0

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Question 91 Mark

The point of intersection of X and Y axes is called:

Answer

Origin.
Solution:
In two dimensions, On the flat coordinate plane, there are two axes,
The vertical y-axis and the horizontal x-axis.
The origin is the point where they intersect.
This point has the coordinates (0, 0) and is usually labelled with the letter O.

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Question 101 Mark

The points (-5, 2) and (2, -5) lie in the:

Answer

II and IV quadrants, respectively.
Solution:
In point (-5, 2), x-coordinate is negative and y-coordinate is positive, so it lies in II quadrant and in point (2, -5),
x- coordinate is positive and y-coordinate is negative, so it lies in IV quadrant.

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Question 111 Mark

The signs of abscissa and ordinate of a point in quadrant IV are:

Answer

(+, -)
Solution:
In the Cartesian plane, if co-ordinate of any point P is P(x, y), then x-coordinate is called the abscissa of the point and, y-coordinate is called ordinate of the point.
The signs of abscissa and ordinate of a point in quadrant IV is (+, -)

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Question 121 Mark

If A (-2, 3) and B(-3, 5) are two given points then (abscissa of A) - (abscissa of B) = ?

Answer

1
Solution:
Abscissa of A - Abscissa of B
= -2 - (-3)
= -2 + 3
= 1

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Question 131 Mark

The abscissa of a point is positive in the:

Answer

Fourth and first quadrant.
Solution:
We know that abscissa is always positive in first and fourth coordinate and ordinate is always positive in first and second coordinate:

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Question 141 Mark

The point whose ordinate is 3 and which lies on the y-axis is:

Answer

(0, 3)
Solution:
Since the point lies on y-axis, so, x = 0.
Hence, the required point is: (0, 3)

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Question 151 Mark

The abscissa of any point on y-axis is:

Answer

0
Solution:
The abscissa of any point on y-axis is always zero. This means that this point hasn't covered any distance on x-axis.

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Question 161 Mark

In Figure, the point identified by the coordinates (-5, 3) is:

Answer

L
Solution:
In point (-5, 3), x-coordinate is negative and y-coordinate is positive, so it will lie in II quadrant. Now, we see that perpendicular distance of L from V-axis is 5 and from X-axis is 3.
So, the required point is L.

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Question 171 Mark

Points (1, -1), (2, -2), (-3, -4), (4, -5)

Answer

Do not lie in the same quadrant.
Solution:
Points (1, -1), (2, -2) and (4, -5) lie in Quadrant IV, but point (-3, -4) lies in Quadrant III.
Hence, all the given points do not lie in the same quadrant.

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Question 181 Mark

Write the correct answer in the following:
If P(5, 1), Q(8, 0), R(0, 4), S(0, 5) and O(0, 0) are plotted on the graph paper, then the point(s) on the x-axis are:

Answer

Q and O
Solution:
We now that, a point lies on X-axis, if its y-coordinate is zero.
So, the points on the axis are Q(8, 0) and O(0, 0).

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Question 191 Mark

The point (0, -4) lies:

Answer

On the negative direction of y-axis
Solution:
Since x = 0 so point lies on y-axis, but value of y is -ve.
So, point lies on -ve direction of y-axis.

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Question 201 Mark

The equation of y-axis is:

Answer

x = 0
Solution:
The value of abscissa or x-corrdinate is always zero at any point on y-axis.
So, x = 0 is the equation of y-axis.

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Question 211 Mark

The abscissa and ordinate of the origin are:

Answer

(0, 0)
Solution:
Absciss = intercept pon X - axis = 0
Ordinate = intercept on Y - axis = 0
⇒ (0, 0) is the answer.

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Question 221 Mark

The perpendicular distance of the point P (4, 3) from x-axis is:

Answer

3
Solution:
The perpendicular distance of any point from x-axis is always equal to the value of ordinate.

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Question 231 Mark

Write the correct answer in the following:
Point (0, -7) lies:

Answer

In the fourth quadrant.
Solution:
In Point (0, -7) co-ordinate of x axis is zero so it lies on y axis.

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Question 241 Mark

Points (2, -3), (4, -5), (5, -9) and (-2, -5).

Answer

Does not lie in same quadrant.
Solution:
Point (2, -3), (4, -5), (5, -9) lies in 4th quadrant, because sign of abscissa and ordinate in 4th quadrant is (+, -).
But point (-2, -5) lies in 3rd quadrant since, sign of abscissa and ordinate in 3rd quadrant is (-, -).

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Question 251 Mark

Which of the following points lie on the line y = 3x – 4?

Answer

(2, 2)
Solution:
When we put x = 2 in the given equation,
Then, y = (3 × 2)–4
y = 6 - 4 = 2, so point is (2, 2)satisfied the given equation,
Hence point (2, 2) will lie on the line y = 3x - 4

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Question 261 Mark

The area of the triangle formed by the points P(0, 1), Q(0, 5) and R(3, 4)is:

Answer

6sq. units
Solution:

PQ = 4 units
Let RS be perpendicular drawn from R to PQ.
Lenght of RS = abscissa of (3, 4)
⇒ RS = 3 units
Area of $\triangle\text{RQP}=\frac{1}{2}\times\text{PQ}\times\text{RS}$
$=\frac{1}{2}\times\text{4}\times\text{3}$
$=6\text{sq. units}.$

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Question 271 Mark

The perpendicular distance of the point P(-2, -3) from the y-axis is:

Answer

2 units
Solution:
Perpendicular distance of any point from y-axis is the given x-coordinate of point,
So distance = 2 units

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Question 281 Mark

Which of the following are the signs of abscissa and ordinate of a point in quadrant?

Answer

(+, +)
Solution:
The signs of abscissa and ordinate of a point in quadrant I are both +ve i.e. (+, +)

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Question 291 Mark

The co-ordinates of two points A and B are (4, 3) and (-5, 3) respectively. The co-ordinates of the point at which the line segment AB meets the y-axis are:

Answer

(0, 3)
Solution:
Since it meets at y-axis, so, abscissa will be zero and we have ordinate = 3 in common so,point will be (0, 3)

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Question 301 Mark

If A(2, 3) and B(-3, 4), then (abscissa of A) - (abscissa of B) is:

Answer

5
Solution:
Here we have, the abscissa of A = 2 and abscissa of B = -3.
So, according to question,
(abscissa of A) - (abscissa of B)
= 2 - (-3)
= 5

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Question 311 Mark

If P(3, 9) and Q(-3, -4), then (abscissa of P) - (ordinate of Q) is:

Answer

7
Solution:
From the given data we have,
The abscissa of P = 3 and ordinate of Q = -4,
So, according to question,
(abscissa of P) - (ordinate of Q)
= 3 - (-4)
= 7

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Question 321 Mark

The co-ordinate of origin is:

Answer

(0, 0)
Solution:
The center of the coordinate system (where the lines intersect) is called the origin.
The axes intersect when both x and y are zero.
The coordinates of the origin are (0, 0).

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Question 331 Mark

Write the correct answer in the following:
Point (-3, 5) lies in the:

Answer

Second quadrant.
Solution:
In the point (-3, 5) abscissa is negative and ordinate is positive. So, it lies in the second quadrant.

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Question 341 Mark

A point whose abscissa and ordinate are 2 and -5 respectively, lies in:

Answer

Fourth quadrant.
Solution:
As we know in the fourth coordinate abscissa is positive and ordinate is negative.

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Question 351 Mark

The point at which the two coordinate axes meet is called the:

Answer

Origin.
Solution:
The point at which the two coordinate axes meet is called the origin.

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Question 361 Mark

The name of the horizontal line drawn to determine the position of any point in the Cartesian plane is:

Answer

x-axis
Solution:
In co-ordinate, we have two axis, one is a horizontal line called x-axis and the other is vertical line called y-axis.
Used to determine the position of any point in Cartesian plane.

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Question 371 Mark

Two points having same abscissa but different ordinates lie on:

Answer

A line parallel to y-axis
Solution:
Two points having same abscissa but different ordinate always make a line which is parallel to the y-axis as abscissa is fixed and the only ordinate keeps changing.

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Question 381 Mark

In Figure, coordinates of P are.

Answer

(-2, 4)
Solution:
Here, given point P lies in II quadrant, so its abscissa will be negative and ordinate wilt be positive. Also, its perpendicular distance from X-axis is 4, so y-coordinate of P is 4 and its perpendicular distance from Y-axis is 2, so x-coordinate is -2. Hence, coordinates of P are (-2, 4).

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Question 391 Mark

The points (-5,3) and (3, -5) lie in the.

Answer

II and IV quadrants respectively.
Solution:
II and IV quadrants respectively, as in II quadrant abscissa is negative and ordinate in positive, on the other hand in IV quadrant abscissa is positive and ordinate is negative.

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Question 401 Mark

The distance of the point (-3, -2) from x-axis is:

Answer

2 units
Solution:
Distance from x-axis is they, co-ordinate of other point So ,here distance = 2,

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Question 411 Mark

The point (-2, 5) lies in:

Answer

2nd quadrant
Solution:
For any point to lie in the second quadrant, Abscissa and ordinate must be (-, +). So the given point (-2, 5) lies in 2nd quadrant.

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Question 421 Mark

The point at which the two co-ordinate axes meet is called the:

Answer

Origin.
Solution:
In co-ordinate system, there are two axes; x-axis and y-axis, point of intersection of x-axis and y-axis is called the origin.

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Question 431 Mark

If a > 0 and b > 0 then the point (a, b) lies in quadrant.

Answer

II
Solution:
Since, x co-ordinate is negative and y co-ordinate is positive, the given point lies in Quadrant II.

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Question 441 Mark

The zero of the polynomial $(x - 2)^2 - (x + 2)^2$ is:

Answer

$(x - 2)^2 - (x + 2)^2$
$= (x - 2 + x + 2) (x - 2 - x - 2) [$Using identity$]$
$a^2 - b^2 = (a + b) (a - b)$
$= (2x) (-4)$
$= -8x$
Then the zero is,
$-8x = 0$
$\Rightarrow x = 0$

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Question 451 Mark

If O(0, 0), A(3, 0), B(3, 4), C(0, 4) are four given points then the figure OABC is a:

Answer

Rectangle.
Solution:
By plotting the given points, we find that figure OABC is a rectangle.

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Question 461 Mark

Signs of the abscissa and ordinate of a point in the second quadrant are respectively.

Answer

(-, +)
Solution:
Abscissa means just the horizontal axis i.e. x axis. Ordinate means just the vertical axis i.e. y axis.
x-corrdinate and y-corrdinate make a point.
The signs of abscissa and ordinate of a point in quadrant II are (-, +).

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Question 471 Mark

Two point having same abscissae but different ordinates lie on:

Answer

A line parallel to y-axis
Solution:
Let two points be (a, b) and (a, c).
If abscissa is same = a
and ordinate is different then all such points will lie on a line parallel to Y
axis because value of X-intercept
i.e. abscissa is fixed.

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Question 481 Mark

The equation of y-axis is:

Answer