📝 How to plot points on coordinate plane (14 MCQs)

📖 From Digital SAT Algebra • 4. Graphs • 14 questions available

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What is How to plot points on coordinate plane?

Definition:
Plotting points on a coordinate plane involves locating and marking a point given by an ordered pair (x, y), using the rectangular coordinate system, where the x-coordinate indicates the horizontal position relative to the origin (positive to the right, negative to the left), and the y-coordinate indicates the vertical position (positive upward, negative downward), and the point is the intersection of the vertical and horizontal lines through those coordinates.

Working:
To plot a point, start at the origin (0,0), move horizontally along the x-axis to the value of x, then move vertically to the value of y; for example, for (2, 3), move 2 units right and 3 units up; for (-3, 1), move 3 units left and 1 unit up; after plotting, the point can be labeled with its coordinates, and multiple points can be plotted to create graphs, and the process is the same for any ordered pair, and it is important to use consistent scaling on the axes.

Example:
A simple example is plotting the points (0, 0) at the origin, (4, 0) on the x-axis, (0, -3) on the y-axis, and (-2, 4) in quadrant II; another example is plotting (1, -1) in quadrant IV, showing how the signs of coordinates determine the quadrant, making plotting straightforward.

Reason:
Plotting points is the most basic skill in coordinate geometry, and it is essential for graphing equations, understanding functions, and interpreting data, making it a core competency in mathematics and science education.

Easy

Medium

Hard

📝 All How to plot points on coordinate plane MCQs

Q1. Which ordered pair represents a point located 4 units left of the $y$ -axis and 3 units above the $x$ -axis?

(4,3)

(-4,3)

✅

(4,-3)

(-3,4)

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: A point left of the $y$ -axis has a negative $x$ -coordinate, while a point above the $x$ -axis has a positive $y$ -coordinate. Therefore, the coordinates must be $(-4,3)$ , not any option with an incorrect sign or reversed order.

Q2. A student says that $(2,-5)$ and $(-5,2)$ represent the same location because they contain the same two numbers. Which response best evaluates the claim?

A.The claim is correct because order does not matter

B.The claim is incorrect because coordinates require a specific order ✅

C.The claim is correct only in Quadrant IV

D.The claim is incorrect because both coordinates must be positive

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The claim is incorrect because an ordered pair assigns the first number to $x$ and the second to $y$ . Thus $(2,-5)$ and $(-5,2)$ locate different points in different quadrants.

Q3. A delivery map uses the intersection of two roads as the origin. A store is 6 blocks east and 2 blocks south of this intersection. Which coordinates should represent the store?

(-6,2)

(6,2)

(-6,-2)

(6,-2)

✅

💡 Difficulty: easy | ✅ Correct: D

📖 Explanation: Moving east corresponds to a positive $x$ -coordinate, while moving south corresponds to a negative $y$ -coordinate. Combining these directions gives $(6,-2)$ , so the store lies in Quadrant IV.

Q4. Why is the point $(0,-7)$ located on an axis rather than inside a quadrant?

A.Its

x

-coordinate is zero, so it lies on the

y

-axis ✅

B.Its

y

-coordinate is negative, so it lies on the

x

-axis

C.Both coordinates are different

D.Zero coordinates always represent the origin

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: A point lies on the $y$ -axis whenever its $x$ -coordinate is zero. Since $(0,-7)$ has no horizontal displacement but is 7 units below the origin, it lies on the negative $y$ -axis.

Q5. Two points are $P=(-3,4)$ and $Q=(-3,-2)$ . Without calculating distance, what can be concluded about their positions?

A.They lie on a horizontal line

B.They lie on a vertical line ✅

C.They are reflections across the

y

-axis

D.They are in the same quadrant

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Both points have the same $x$ -coordinate, $-3$ . Therefore, they are directly above and below one another on the same vertical line. Their different $y$ -coordinates determine their different vertical positions.

Q6. A robot starts at $(-2,3)$ , moves 5 units right, and then 4 units down. Which ordered pair represents its final position?

(3,-1)

✅

(-7,7)

(3,7)

(-6,8)

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Moving 5 units right changes the $x$ -coordinate from $-2$ to $3$ . Moving 4 units down changes the $y$ -coordinate from $3$ to $-1$ . Therefore, the robot ends at $(3,-1)$ .

Q7. A rectangular garden has corners at $(-4,2)$ , $(3,2)$ , $(3,-1)$ , and $(-4,-1)$ . Which statement correctly describes the garden's orientation?

A.Its left and right sides have equal

x

-coordinates respectively ✅

B.Its top and bottom sides have equal

x

-coordinates

C.All corners lie in the same quadrant

D.Its opposite corners must have identical coordinates

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The two left-side and right-side vertices share their respective $x$ -coordinates, creating vertical sides. The vertices with $y=2$ form the top side, while those with $y=-1$ form the bottom side.

Q8. A student plots $(-5,-2)$ in Quadrant II. What mistake did the student most likely make?

A.They treated the negative

x

-coordinate as positive

B.They treated the negative

y

-coordinate as positive ✅

C.They reversed the coordinates

D.They placed the point on the

y

-axis

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Quadrant II contains points with negative $x$ -coordinates and positive $y$ -coordinates. Since $(-5,-2)$ has both coordinates negative, it belongs to Quadrant III. The likely mistake was treating $y=-2$ as positive.

Q9. A map shows points $A=(-2,5)$ , $B=(4,5)$ , $C=(4,-3)$ , and $D=(-2,-3)$ . A student claims that $A$ and $C$ are vertically aligned. Is the claim correct?

A.Yes, because they have opposite signs

B.Yes, because both are corner points

C.No, because their

x

-coordinates are different ✅

D.No, because their

y

-coordinates are different

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: Vertical alignment requires equal $x$ -coordinates. Point $A$ has $x=-2$ , while point $C$ has $x=4$ . Although they are opposite corners of the rectangle, they are not vertically aligned.

Q10. On a coordinate grid, point $R$ is 3 units right of the $y$ -axis and 6 units below the $x$ -axis. Point $S$ is 3 units left of the $y$ -axis and 6 units above the $x$ -axis. What relationship best describes $R$ and $S$ ?

A.They are reflections across the

x

-axis

B.They are reflections across the

y

-axis

C.They are reflections through the origin ✅

D.They are unrelated because they occupy different quadrants

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: Point $R$ is $(3,-6)$ , while point $S$ is $(-3,6)$ . Both coordinates change signs, which means each point is the opposite of the other. Therefore, they are reflections through the origin.

Q11. A graph shows a point at $(-4,0)$ . A student describes it as being 4 units below the origin. Which correction is most accurate?

A.It is 4 units above the origin

B.It is 4 units left of the origin ✅

C.It is 4 units right of the origin

D.It is 4 units below the

y

-axis

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Because the $x$ -coordinate is $-4$ and the $y$ -coordinate is zero, the point lies on the negative $x$ -axis. It is therefore 4 units left of the origin, not below it.

Q12. A graphing program receives the coordinates $(7,-4)$ , but its user accidentally enters $(-7,4)$ . Relative to the intended point, where will the new point appear?

A.It will be reflected across the

x

-axis

B.It will be reflected across the

y

-axis

C.It will be reflected through the origin ✅

D.It will move only 11 units vertically

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: Changing $(7,-4)$ to $(-7,4)$ reverses the signs of both coordinates. Reversing both coordinates places the new point exactly opposite the original point across the origin.

Q13. Four points are plotted: $A=(2,3)$ , $B=(-2,3)$ , $C=(-2,-3)$ , and $D=(2,-3)$ . A student concludes that $A$ and $C$ are the only pair that are equally far from both axes. Which evaluation is correct?

A.The student is correct

B.Only

B

and

D

satisfy the condition

C.All four points satisfy the condition ✅

D.Only

A

and

D

satisfy the condition

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: For each point, the absolute values of the coordinates are $2$ and $3$ . Thus every point is 2 units from the $y$ -axis and 3 units from the $x$ -axis. The sign changes alter location but not these distances.

Q14. A point $P$ has coordinates $(a,b)$ , where $a<0$ and $b>0$ . Another point $Q$ is obtained by changing only the sign of $b$ . If neither coordinate is zero, where must $P$ and $Q$ lie?

A.Quadrants I and II

B.Quadrants II and III ✅

C.Quadrants III and IV

D.Quadrants I and IV

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: Since $a<0$ and $b>0$ , point $P$ lies in Quadrant II. Changing only the sign of $b$ makes $Q=(a,-b)$ , giving a negative $x$ and negative $y$ , so $Q$ lies in Quadrant III.

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