Orienting Yourself: The Use of Coordinates MCQs for UPSC Prelims
100 practice questions covering Orienting Yourself: The Use of Coordinates, organised into 0 topics.
100 questions include a written explanation.
Pick a topic below, or try the samples first.
Sample questions
Q1
easy
Are the three points $(0,\ 0)$, $(3,\ 0)$ and $(9,\ 0)$ collinear?
ANo, because the three points are all different from one another
BYes, because $0+3+9=12$
CIt cannot be decided without plotting them on graph paper
DYes, because all three lie on the $x$-axis, which is itself a straight line
Show answer and explanation
Correct answer: D - Yes, because all three lie on the $x$-axis, which is itself a straight line
Each of the three has second coordinate $0$, so all of them lie on the $x$-axis, and points sitting on one straight line are collinear. Being different points does not prevent them from lying on a line. The sum $12$ plays no part in the test, and once the shared second coordinate is noticed no plotting is needed.
Q2
medium
Assertion (A): The point $(0,\ -6)$ lies on the $y$-axis. Reason (R): A point whose first coordinate is $0$ stands at zero distance from the $y$-axis, so it lies on that axis. Choose the correct option.
ABoth A and R are true, and R is the correct explanation of A
BBoth A and R are true, but R is not the correct explanation of A
CA is true, but R is false
DA is false, but R is true
Show answer and explanation
Correct answer: A - Both A and R are true, and R is the correct explanation of A
(A) is true, since $(0,\ -6)$ has first coordinate $0$ and sits six units below the origin along the $y$-axis. (R) states the general test and is true as well: the first coordinate measures horizontal distance from the $y$-axis, so a $0$ there puts the point on the axis. That test is exactly why (A) holds, so (R) explains (A).
Q3
easy
Using the distance formula on $A(2,\ 5)$ and $B(7,\ 9)$ gives the same number as using it on $B$ and $A$. Why does that happen?
AReversing the order only changes the sign of each coordinate difference, and a number and its negative have the same square.
BBecause the formula may be used only when all the coordinates are positive.
CBecause $A$ and $B$ happen to have the same coordinates as each other.
DBecause reversing the order changes the sign of the distance but not its size.
Show answer and explanation
Correct answer: A - Reversing the order only changes the sign of each coordinate difference, and a number and its negative have the same square.
Swapping the points turns each difference $d$ into $-d$, and $(-d)^2=d^2$, so the two squares under the root are unchanged and the result is identical. The formula works perfectly well with negative coordinates, the two points here are plainly different, and a distance is never negative, so there is no sign for the swap to change.
Q4
easy
Find the distance between the origin and the point $(6,\ 8)$.
A$10$ units
B$14$ units
C$48$ units
D$2$ units
Show answer and explanation
Correct answer: A - $10$ units
The horizontal step is $6$ and the vertical step is $8$, so the distance is $\sqrt{6^2+8^2}=\sqrt{36+64}=\sqrt{100}=10$ units. Adding the two steps gives $14$, multiplying them gives $48$ and subtracting them gives $2$. Only the square root of the sum of the squares measures the direct slanting join.
Q5
medium
Three vertices of a rectangle with sides parallel to the axes are $(0,\ 0)$, $(0,\ 9)$ and $(4,\ 9)$, drawn with $1$ unit $=1\ \text{cm}$. Give the fourth vertex and the perimeter of the rectangle.
A$(4,\ 0)$ and $13\ \text{cm}$
B$(9,\ 4)$ and $26\ \text{cm}$
C$(4,\ 0)$ and $36\ \text{cm}$
D$(4,\ 0)$ and $26\ \text{cm}$
Show answer and explanation
Correct answer: D - $(4,\ 0)$ and $26\ \text{cm}$
The first coordinates are $0$ and $4$ and the second are $0$ and $9$, so the missing vertex is $(4,\ 0)$. The sides then measure $4\ \text{cm}$ and $9\ \text{cm}$, giving a perimeter of $2(4+9)=26\ \text{cm}$. Adding the sides once only gives $13$, multiplying them gives the area $36$, and $(9,\ 4)$ swaps the coordinates of the missing corner.
Q6
medium
A student plots points with the scale $1\ \text{cm}=5$ units. Measured from the origin, where on the paper does the point $(20,\ -15)$ fall?
A$4\ \text{cm}$ to the right and $3\ \text{cm}$ down
B$20\ \text{cm}$ to the right and $15\ \text{cm}$ down
C$4\ \text{cm}$ to the right and $3\ \text{cm}$ up
D$100\ \text{cm}$ to the right and $75\ \text{cm}$ down
Show answer and explanation
Correct answer: A - $4\ \text{cm}$ to the right and $3\ \text{cm}$ down
With $5$ units to the centimetre, $20$ units measures $20 \div 5 = 4\ \text{cm}$ and $15$ units measures $15 \div 5 = 3\ \text{cm}$. The second coordinate is negative, so those $3\ \text{cm}$ go downwards. Using the raw numbers ignores the scale, moving upwards mistakes the sign, and multiplying by $5$ instead of dividing gives a drawing far too large for the page.
Practice the full Orienting Yourself: The Use of Coordinates bank free
All 100 questions with timed practice, instant scoring, and explanations. Free forever.