12 multiple-choice questions, progressively harder.
On which axis does a point lie if its y-coordinate is 000?
Solution
Correct answer: B
A y-coordinate of 000 means no up-or-down movement, so the point sits on the horizontal axis.
y=0 ⇒ on the x-axis.y = 0 \;\Rightarrow\; \text{on the x-axis}.y=0⇒on the x-axis.
A rectangle has horizontal sides of length 666 and vertical sides of length 444, with corners on the grid. What is its perimeter?
Correct answer: C
Use the rectangle perimeter formula with l=6l = 6l=6 and w=4w = 4w=4.
P=2(l+w)=2(6+4)=2×10=20.P = 2(l + w) = 2(6 + 4) = 2 \times 10 = 20.P=2(l+w)=2(6+4)=2×10=20.
The perimeter is 202020 units.
Which point lies in Quadrant IV?
Correct answer: A
Quadrant IV is the lower-right region, with a positive x-coordinate and a negative y-coordinate.
(7,−3): (+,−) ⇒ Quadrant IV.(7, -3): \; (+, -) \;\Rightarrow\; \text{Quadrant IV}.(7,−3):(+,−)⇒Quadrant IV.
Only (7,−3)(7, -3)(7,−3) matches that sign pattern.
Points (−2,−5)(-2, -5)(−2,−5) and (−2,4)(-2, 4)(−2,4) share a coordinate. What is the distance between them?
Correct answer: D
Both points have x=−2x = -2x=−2, so the segment is vertical. Subtract the y-coordinates and take the absolute value.
∣4−(−5)∣=∣4+5∣=9.|4 - (-5)| = |4 + 5| = 9.∣4−(−5)∣=∣4+5∣=9.
They are 999 units apart.
Reflect the point (−6,1)(-6, 1)(−6,1) across the y-axis. What are the new coordinates?
Reflecting across the y-axis keeps the y-coordinate and flips the sign of the x-coordinate.
(−6,1)→(6,1).(-6, 1) \to (6, 1).(−6,1)→(6,1).
The point stays at the same height but moves to the same distance on the other side of the y-axis.
The point (0,0)(0, 0)(0,0) belongs to which quadrant?
The origin sits on both axes, and points on an axis belong to no quadrant.
(0,0) ⇒ no quadrant.(0, 0) \;\Rightarrow\; \text{no quadrant}.(0,0)⇒no quadrant.
The quadrants are the open regions strictly between the axes.
Which point is on the x-axis?
A point is on the x-axis exactly when its y-coordinate is 000.
(−4,0): y=0 ⇒ on the x-axis.(-4, 0): \; y = 0 \;\Rightarrow\; \text{on the x-axis}.(−4,0):y=0⇒on the x-axis.
The others have nonzero y-coordinates.
Plotting (2,−7)(2, -7)(2,−7) lands in which quadrant?
The x-coordinate is positive and the y-coordinate is negative.
(+,−) ⇒ Quadrant IV.(+, -) \;\Rightarrow\; \text{Quadrant IV}.(+,−)⇒Quadrant IV.
Starting at the origin, you move 333 left and then 666 up. In which quadrant do you land?
Moving 333 left gives x=−3x = -3x=−3 and moving 666 up gives y=6y = 6y=6, so the point is (−3,6)(-3, 6)(−3,6).
(−,+) ⇒ Quadrant II.(-, +) \;\Rightarrow\; \text{Quadrant II}.(−,+)⇒Quadrant II.
Which statement about the points (4,0)(4, 0)(4,0) and (0,4)(0, 4)(0,4) is correct?
Order matters, so these are different points. The first, (4,0)(4, 0)(4,0), has y=0y = 0y=0 and lies on the x-axis; the second, (0,4)(0, 4)(0,4), has x=0x = 0x=0 and lies on the y-axis.
(4,0)≠(0,4).(4, 0) \ne (0, 4).(4,0)=(0,4).
Neither is in a quadrant, since each lies on an axis.
A point in Quadrant II is reflected across the y-axis. In which quadrant does its image land?
A Quadrant II point has the pattern (−,+)(-, +)(−,+). Reflecting across the y-axis flips the sign of the x-coordinate, giving (+,+)(+, +)(+,+).
(−,+)→(+,+) ⇒ Quadrant I.(-, +) \to (+, +) \;\Rightarrow\; \text{Quadrant I}.(−,+)→(+,+)⇒Quadrant I.
Which point is exactly 444 units to the right of (−1,2)(-1, 2)(−1,2)?
Moving right changes only the x-coordinate, adding 444 to it; the y-coordinate stays the same.
(−1+4, 2)=(3,2).(-1 + 4, \; 2) = (3, 2).(−1+4,2)=(3,2).
So the point 444 units to the right is (3,2)(3, 2)(3,2).
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