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Maths M.C.Q

Coordinate Geometry · Gujarat Board (GSEB) STD 9 (GSEB - English Medium). 22 questions.

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M.C.Q

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22 questions · timed · auto-graded

MCQ 11 Mark
If $a > 0$ and $b > 0$ then the point $(a, b)$ lies in quadrant.
  • A
    $IV$
  • ✓
    $II$
  • C
    $III$
  • D
    None of these.
Answer
Correct option: B.
$II$
Since, $x$ co-ordinate is negative and $y$ co-ordinate is positive, the given point lies in Quadrant $II$.
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MCQ 21 Mark
The ordinate of every point on the $x$-axis is:
  • A
    $1$
  • B
    $-1$
  • ✓
    $0$
  • D
    Any real numbers.
Answer
Correct option: C.
$0$
The ordinate ($y$ co-ordinate) of every point on the $x$-axis is $0$.
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MCQ 31 Mark
A point both of whose coordinates are negative lies in quadrant.
  • A
    $I$
  • B
    $II$
  • ✓
    $III$
  • D
    $IV$
Answer
Correct option: C.
$III$

A point both of whose coordinates are negative, that is, of the from $(-, -)$ lies in quadrant $III$.
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MCQ 41 Mark
The point at which the two coordinate axes meet is called the:
  • A
    Abscissa.
  • B
    Ordinate.
  • ✓
    Origin.
  • D
    Quadrant.
Answer
Correct option: C.
Origin.
The point at which the two coordinate axes meet is called the origin.
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MCQ 51 Mark
Abcissa of a point is positive in:
  • A
    $I$ and $II$ quadrant.
  • ✓
    $I$ and $IV$ quadrant.
  • C
    $I$ quadrant only.
  • D
    $II$ quadrant only.
Answer
Correct option: B.
$I$ and $IV$ quadrant.

Absissa of a point is positive when the points are of the form $(+, +)$ and $(+, -).$
So, the absissa of the point is positive in quadrant $I$ and $IV$.
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MCQ 61 Mark
If $O(0, 0), A(3, 0), B(3, 4), C(0, 4)$ are four given points then the figure $OABC$ is a:
  • A
    Square.
  • ✓
    Rectangle.
  • C
    Trapezium.
  • D
    Rhombus.
Answer
Correct option: B.
Rectangle.
By plotting the given points, we find that figure $OABC$ is a rectangle.
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MCQ 71 Mark
Which of the following points does not lie in any quadrant?
  • A
    $(1, 7)$
  • B
    $(2, 10)$
  • C
    $(-1, 1)$
  • ✓
    $(4, 12)$
Answer
Correct option: D.
$(4, 12)$
For the point to lie on the line $y = 3x + 4$, it has to satisfy the equation of the line.
Putting $x = 1$, in $y = 3x + 4$, we get $y = 3(1) + 4 \Rightarrow y = 7$
So, the point satisfies the equation and hence lies on the given line.
Putting $x = 2$, in $y = 3x + 4$, we get $y = 3(2) + 4 \Rightarrow y = 10$
So, the point satisfies the equation and hence lies on the given line.
Putting $x = 1$, in $y = 3x + 4$, we get $y = 3(-1) + 4 \Rightarrow y = 1$
So, the point satisfies the equation and hence lies on the given line.
Putting $x = 4$, in $y = 3x + 4$, we get $y = 3(4) + 4 \Rightarrow y = 16$
But $y = 12$.
So, the point not satisfy the equation and hence lies on the given line.
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MCQ 81 Mark
Point $(-7, 0)$ lies.
  • ✓
    On the negative direction of $x$-axis.
  • B
    On the negative direction of $y$-axis.
  • C
    In the $III$ quadrant.
  • D
    In the $IV$ quadrant.
Answer
Correct option: A.
On the negative direction of $x$-axis.
Point $(-7, 0)$ lies on negative direction of the $x$-axis as its $x$ co-ordinate is negative and $y$ co-ordinate is zero.
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MCQ 91 Mark
If $A (-2, 3)$ and $B(-3, 5)$ are two given points then (abscissa of $A$) - (abscissa of $B$) = ?
  • A
    $-2$
  • ✓
    $1$
  • C
    $-1$
  • D
    $2$
Answer
Correct option: B.
$1$
Abscissa of $A$ - Abscissa of $B$
$= -2 - (-3)$
$= -2 + 3$
$= 1$
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MCQ 101 Mark
The area of $\triangle\text{AOB}$ having vertices $A(0, 6), O(0, 0)$ and $B(6, 0)$ is:
  • A
    $12$sq units.
  • B
    $36$sq units.
  • ✓
    $18$sq units.
  • D
    $24$sq units.
Answer
Correct option: C.
$18$sq units.

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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MCQ 111 Mark
Points $(1, -1), (2, -2), (-3, -4), (4, -5)$
  • ✓
    All lie in the $II$ quadrant.
  • B
    All in the $III$ quadrant.
  • C
    All lie in the $IV$ quadrant.
  • D
    Do not lie in the same quadrant.
Answer
Correct option: A.
All lie in the $II$ quadrant.
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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MCQ 121 Mark
In the which quadrant does the point $(-7, -4)$ lie?
  • A
    $IV$
  • B
    $II$
  • ✓
    $III$
  • D
    None of these.
Answer
Correct option: C.
$III$
Since, both the coordinates of given point are negative, it lies in Quadrant $III$.
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MCQ 131 Mark
The point (other than origin) for which abscissa is equal to the ordinate will lie in quadrant.
  • A
    $I$ only
  • B
    $I$ or $II$
  • ✓
    $I$ or $III$
  • D
    $II$ or $IV$
Answer
Correct option: C.
$I$ or $III$

The points are same when they are of the form $(m, m)$ or $(-n, -n)$.
This happens only in quadrant $I$ and quadrant $III$.
So, the points (other than the origin) for which the abscissa is equal to the ordinate lie in quadrant $I$ and quadrant $III$.
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MCQ 141 Mark
The point which lies on the y-axis at a distance of $5$ units in the negative direction of the $y$-axis is:
  • A
    $(-5, 0)$
  • ✓
    $(0, -5)$
  • C
    $(5, 0)$
  • D
    $(0, 5)$
Answer
Correct option: B.
$(0, -5)$
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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MCQ 151 Mark
Which of the following points lies on the line $y = 2x + 3?$
  • A
    $(2, 8)$
  • ✓
    $(3, 9)$
  • C
    $(4, 12)$
  • D
    $(5, 15)$
Answer
Correct option: B.
$(3, 9)$
For the point to lie on the line $y = 2x + 3$, it has to satisfy the equation of the line.
Putting $x = 2$, in $y = 2x + 3$, we get $y = 2(2) + 3 \Rightarrow y = 7$
But $y = 8$.
So, the point does not satisfy the equation and hence does not lie on the given line.
Putting $x = 3,$ in $y = 2x + 3,$ we get $y = 2(3) + 3 \Rightarrow y = 9$
So, the point satisfies the equation and hence lies on the given line.
Putting $x = 4,$ in $y = 2x + 3$, we get $y = 2(4) + 3 \Rightarrow y = 11$
But $y = 12$.
So, the point does not satisfy the equation and hence does not lie on the given line.
Putting $x = 5$, in $y = 2x + 3,$ we get $y = 2(5) + 3 \Rightarrow y = 13$
But $y = 15$.
So, the point does not satisfy the equation and hence does not lie on the given line.
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MCQ 161 Mark
If $x > 0$ and $y < 0$ then the point $(x, y)$ lies in quadrant.
  • A
    $I$
  • B
    $III$
  • C
    $II$
  • ✓
    $IV$
Answer
Correct option: D.
$IV$

Points of the type $(+, -)$ lie in the $4th$ quadrant.
Since $x > 0$ and $y < 0$, the point $(x, y)$ lies in quadrant $IV$.
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MCQ 171 Mark
If the $y$-coordinate of a point is zero then this point always lies.
  • A
    On the $y$-axis.
  • ✓
    On the $x$-axis.
  • C
    In the $I$ quadrant.
  • D
    In the $IV$ quadrant.
Answer
Correct option: B.
On the $x$-axis.
If the $y$-coordinate of a point is zero then this point always lies on the $x$-axis.
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MCQ 181 Mark
The points $(-5, 3)$ and $(3, -5)$ lie in the.
  • A
    same quadrant
  • B
    $II$ and $III$ quadrants respectively.
  • ✓
    $II$ and $IV$ quadrants respectively.
  • D
    $IV$ and $II$ quadrants respectively.
Answer
Correct option: C.
$II$ and $IV$ quadrants respectively.
For point $(-5, 3)$, the $x$ co-ordinate is negative and the $y$ co-ordinate is positive. Hence, it lies in Quadrant $II$.
For point $(3, -5)$, the $x$ co-ordinate is positive and the $y$ co-ordinate is negative. Hence, it lies in Quadrant $IV$.
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MCQ 191 Mark
The point at whose ordinate is $3$ and which lies on the $y$-axis is:
  • A
    $(3, 0)$
  • ✓
    $(0, 3)$
  • C
    $(3, 3)$
  • D
    $(1, 3)$
Answer
Correct option: B.
$(0, 3)$
If a point lies on $y$-axis, then its abscissa is $0$.
Hence, the point whose ordinate is $3$ and which lies on the $y$-axis is $(0, 3)$.
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MCQ 201 Mark
Point $(0, -8)$ lies.
  • A
    In the $II$ quadrant.
  • B
    In the $IV$ quadrant.
  • C
    On the $x$-axis.
  • ✓
    On the $y$-axis.
Answer
Correct option: D.
On the $y$-axis.
Point $(0, -8)$ lies on $y$-axis as its $x$ co-ordinate is $0$.
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MCQ 211 Mark
Which of the following points does not lie in any quadrant?
  • A
    $(3, -6)$
  • B
    $(-3, 4)$
  • C
    $(5, 7)$
  • ✓
    $(0, 3)$
Answer
Correct option: D.
$(0, 3)$
The abscissa of point $(0, 3)$ is $0$. Hence, it lies on $y$-axis.
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MCQ 221 Mark
The perpendicular distance of the point $A(3, 4)$ from the $y$-axis is:
  • ✓
    $3$
  • B
    $4$
  • C
    $5$
  • D
    $7$
Answer
Correct option: A.
$3$
The perpendicular distance of the point $A(3, 4)$ from the $y$-axis is $3$ units.
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