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MATHS M.C.Q

Coordinate Geometry · Rajasthan Board (RBSE) STD 9 (Rajasthan - English Medium). 15 questions.

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15 questions · timed · auto-graded

Question 11 Mark
The area of the triangle formed by the points A(2, 0), B(6, 0) and C(4, 6) is:
  1. 24sq. unit
  2. 12sq. unit
  3. 10sq. unit
  4. None of these
Answer
  1. 12sq. unit
Solution:

Let CD be perpendicular drawn from C to AB.
The length of the perpendicular will be equal to the ordinate of point C.
⇒ CD = 6 unit
AB = 4 unit
Now, area of $\triangle\text{ABC}=\frac{1}{2}\times\text{Base}\times\text{height}$
$\triangle\text{ABC}=\frac{1}{2}\times\text{5}\times\text{6}$
$12\text{sq. units}$ 
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Question 21 Mark
A point whose abscissa is -3 and ordinate 2 lies in:
  1. First quadrant.
  2. Second quadrant.
  3. Third quadrant.
  4. Fourth quadrant.
Answer
  1. Second quadrant
Solution:
If absciss = -3
Intercept on Y axis is = 2
Y > 0
So, Point is in Second Quadrant.
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Question 31 Mark
A point whose abscissa and ordinate are 2 and -5 respectively, lies in:
  1. First quadrant.
  2. Second quadrant.
  3. Third quadrant.
  4. Fourth quadrant.
Answer
  1. Fourth quadrant
Solution:
Abscissa is = 2(positive intercept on X-axis)
and ordinate = -5(negative intercept on Y-axis)
so X-value is positive and Y-value is negative, i.e. Fourth Quadrant.
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Question 41 Mark
The ordinate of any point on x-axis is:
  1. 0
  2. 1
  3. -1
  4. Any number
Answer
  1. 0
Solution:
On X-axis, all points have their Y-intercept = 0
So their ordinate = 0
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Question 51 Mark
The abscissa of a point is positive in the:
  1. First and Second quadrant.
  2. Second and Third quadrant.
  3. Third and Fourth quadrant.
  4. Fourth and First quadrant.
Answer
  1. Fourth and First quadrant
Solution:
Abscissa = Intercept on X-axis
If intercept on X-axis is positive, means First and Fourth quadrant
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Question 61 Mark
The perpendicular distance of the point P(4, 3) from y-axis is:
  1. 4
  2. 3
  3. 5
  4. None of these
Answer
  1. 4
Solution:
If we draw a perpendicular from point P(4, 3) to Y-axis, the measure of perpendicular is equal to abscissa of point P.
So perpendicular distance fprm Y-axis = abscissa = 4
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Question 71 Mark
Two point having same abscissae but different ordinates lie on:
  1. x-axis
  2. a-axis
  3. A line parallel to y-axis
  4. A line parallel to x-axis
Answer
  1. 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 81 Mark
The abscissa and ordinate of the origin are:
  1. (0, 0)
  2. (1, 0)
  3. (0, 1)
  4. (1, 1)
Answer
  1. (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 91 Mark
The perpendicular distance of the point P(4, 3) from x-axis is:
  1. 4
  2. 3
  3. 5
  4. None of these
Answer
  1. 3
Solution:
If perpendicular drawn from P to X-axis, then the perpendicular is equal to measure of ordinate of point P.
So, perpendicular distance of point P form X-axis = 3
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Question 101 Mark
Points (-4, 0) and (7, 0) lie:
  1. On x-axis.
  2. Y-axis.
  3. In first quadrant.
  4. In second quadrant.
Answer
  1. On x-axis
Solution:
In (-4, 0) and (7, 0),
measure of ordinate = 0
That means, intercept on Y-axis = 0
So, points lies on X-axis.
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Question 111 Mark
The distance of the point P(4, 3) from the origin is:
  1. 4
  2. 3
  3. 5
  4. 7
Answer
  1. 5
Solution:
Point P(4, 3) and Origin O(0, 0)
Required distance $=\text{OP}=\sqrt{(0-4)^2+(0-3)^2}$ (by distance formula)
$=\sqrt{16+9}$
$=\sqrt{25}$
$=5$
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Question 121 Mark
The measure of the angle between the coordinate axes is:
  1. 0º
  2. 90º
  3. 180º
  4. 360º
Answer
  1. 90º
Solution:
The angle between the co-ordinate axes is 90º because $\text{X}-\text{axis}\perp\text{Y}-\text{axis}.$
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Question 131 Mark
The point of intersect of the coordinate axes is:
  1. Ordinate
  2. Abscissa
  3. Quadrant
  4. Origin
Answer
  1. Origin
Solution:
The point of intersection of co-ordinate axes i.e. X-axis and Y-axis is (0, 0), which is called origin.
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Question 141 Mark
The area of the triangle formed by the points P(0, 1), Q(0, 5) and R(3, 4)is:
  1. 16sq. units
  2. 6sq. units
  3. 4sq. units
  4. 6sq. units
Answer
  1. 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 151 Mark
The abscissa of any point on y-axis is:
  1. 0
  2. 1
  3. -1
  4. Any number
Answer
  1. 0
Solution:
Every point on Y-axis have X-intercept = 0
Thus, their abscissa = 0
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