Class 9 Orienting Yourself: The Use of Coordinates Mock Test (CBSE)

Topics in Orienting Yourself: The Use of Coordinates

• Locating points and directions
• The 2-D Cartesian coordinate system
• Coordinates of a point and quadrants
• Distance between two points in the plane
• Mid-point of a line segment

Orienting Yourself: The Use of Coordinates practice questions with answers

1. Q1Multiple choice·1 mark
   The mid-point of the line segment joining the points $(2, 3)$ and $(4, 7)$ is:

   1. (a)$(3, 5)$
   2. (b)$(2, 4)$
   3. (c)$(6, 10)$
   4. (d)$(1, 2)$
   Show answer and step marks

   1. Correct option: (a) $(3, 5)$+1

   Answer: (a)
2. Q2Multiple choice·1 mark
   The point $P(x, y)$ is equidistant from the points $A(3, 6)$ and $B(-3, 4)$. If $P$ lies on the line $y = 2x$, then the coordinates of $P$ are:

   1. (a)$(1, 2)$
   2. (b)$(2, 4)$
   3. (c)$(-1, -2)$
   4. (d)$(3, 6)$
   Show answer and step marks

   1. Correct option: (a) $(1, 2)$+1

   Answer: (a)
3. Q3Multiple choice·1 mark
   What is the distance of the point $(3, 4)$ from the origin?

   1. (a)$3$
   2. (b)$4$
   3. (c)$5$
   4. (d)$7$
   Show answer and step marks

   1. Correct option: (c) $5$+1

   Answer: (c)
4. Q4Multiple choice·1 mark
   In which quadrant does the point $(-3, -5)$ lie?

   1. (a)First quadrant
   2. (b)Second quadrant
   3. (c)Third quadrant
   4. (d)Fourth quadrant
   Show answer and step marks

   1. Correct option: (c) Third quadrant+1

   Answer: (c)
5. Q5Short answer·3 marks
   The points $P(-3, 5)$, $Q(4, -2)$, $R(-6, -7)$ and $S(8, 3)$ are plotted on a Cartesian plane. (a) In which quadrant does the point $Q$ lie? [1] (b) Which of the four points lies in the quadrant where both coordinates are negative? [1] (c) The point $K(-5, 2)$ is also plotted. Is $K$ in the same quadrant as $P$? Give a reason. [1]
   Show answer and step marks

   1. (a) For Q(4, −2), the abscissa is positive and the ordinate is negative, so Q lies in the fourth quadrant (Quadrant IV).+1
   2. (b) Quadrant III is where both coordinates are negative. R(−6, −7) has both coordinates negative, so the point is R.+1
   3. (c) K(−5, 2) has a negative abscissa and a positive ordinate, so it lies in Quadrant II. P(−3, 5) also has a negative abscissa and a positive ordinate, so it lies in Quadrant II. Hence K is in the same quadrant as P, since the signs of their coordinates are the same.+1

   Answer: (a) Quadrant IV; (b) R(−6, −7); (c) Yes, both K and P lie in Quadrant II, since both have a negative x-coordinate and a positive y-coordinate.
6. Q6Short answer·3 marks
   If the mid-point of the line segment joining the points $A(x, 5)$ and $B(7, -3)$ is $P(3, y)$, find the values of $x$ and $y$. Hence, find the distance $AB$.
   Show answer and step marks

   1. Using the mid-point formula for the x-coordinate: $3 = \frac{x + 7}{2} \Rightarrow 6 = x + 7 \Rightarrow x = -1$+1
   2. Using the mid-point formula for the y-coordinate: $y = \frac{5 + (-3)}{2} = 1$+1
   3. Calculating the distance $AB$ with $A(-1, 5)$ and $B(7, -3)$: $AB = \sqrt{(7 - (-1))^2 + (-3 - 5)^2} = \sqrt{64 + 64} = \sqrt{128} = 8\sqrt{2}$ units+1

   Answer: $x = -1$, $y = 1$, and distance $AB = 8\sqrt{2}$ units

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