A two-dimensional surface formed by two perpendicular number lines — the horizontal x-axis and the vertical y-axis — intersecting at the origin (0,0). Every point on the plane is uniquely identified by an ordered pair (x,y) giving its horizontal and vertical distances from the origin.
Like a map with street numbers—the address (3,2) is 3 right, 2 up.
Showing a random 20 of 50 problems.
Example 1
challenge
A triangle has vertices (0,0), (4,0), (4,3). Find its area.Right triangle with base 4 and height 3; area = ½ × 4 × 3 = 6.
Example 2
challenge
Find the point on the x-axis equidistant from (1,2) and (5,4).
Example 3
medium
A point starts at (2,−1), moves 3 units right and 4 units up. Where does it end?
Example 4
challenge
Three points (1,1), (2,3), (3,5) — are they collinear?Equal slopes between consecutive points confirm collinearity.
Example 5
medium
Reflect (6,−2) over the x-axis.Reflection over x-axis: (6, −2) → (6, 2).
Example 6
easy
Is the point (−6,0) on the x-axis or the y-axis?
Example 7
medium
Rotate the point (3,0) by 90∘ counterclockwise about the origin.
Example 8
medium
Point (a,b) is in Quadrant III. In which quadrant is (−a,b)?
Example 9
easy
On which axis does the point (0,−8) lie?
Example 10
easy
On which axis does (7,0) lie?y = 0 means (7, 0) lies on the x-axis.
Example 11
easy
What is the sign pattern of coordinates in Quadrant II?
Example 12
easy
In which quadrant is the point (5,−2)?Sign pattern (+, −) places (5, −2) in Quadrant IV.
Example 13
medium
Find the midpoint of the segment from (−4,−6) to (10,2).
Example 14
challenge
Find the area of the quadrilateral with vertices (0,0), (4,0), (5,3), (1,3).Parallelogram with base 4 and height 3; area = 4 × 3 = 12.
Example 15
easy
How far to the left of the y-axis is (−7,3)?
Example 16
medium
Find the midpoint of the segment from (−5,3) to (7,−9).Midpoint M(1, −3) of segment from A(−5, 3) to B(7, −9).
Example 17
medium
Which is closer to the origin: (6,8) or (7,7)?
Example 18
easy
Are (2,3) and (3,2) the same point?
Example 19
easy
What are the coordinates of the origin?
Example 20
medium
Are the points (2,3), (4,3), (4,7) vertices of a right triangle?Horizontal leg PQ and vertical leg QR meet at a right angle at Q.