Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Later problems draw polygons from their vertices and find side lengths. The final six mix maps, rectangles and reflection, so sketch a grid before computing.
Standards: 6.NS.C.6b, 6.NS.C.6c, 6.NS.C.8, 6.G.A.3 · Level: Grade 6
Problem 1 Reading coordinates ★★★
Write the ordered pair for each point A, B, C and D.
Problem 2 Naming quadrants ★★★
Name the quadrant of each point: (7, −3), (−2, −8), (−6, 4), (1.5, 9).
Problem 3 Points on the axes ★★★
Describe where each point lies: (0, −4), (5, 0), (−3, 0), (0, 6).
Problem 4 Reflecting a point ★★★
A kite icon sits at (8, 3). Where does it land when flipped over the x-axis, and, separately, when flipped over the y-axis?
Problem 5 Two reflections ★★★
- Reflect (−6, 2) across the y-axis.
- Reflect (−7, −3) across the x-axis.
Problem 6 Horizontal distance ★★★
A drone flies straight from (−9, 6) to (5, 6). How many units does it travel?
Problem 7 Vertical distance, same signs ★★★
Find the distance between (5, −9) and (5, −2).
Problem 8 Rational coordinates ★★★
Write the coordinates of points E, F and G, then name the quadrant or axis of each.
Problem 9 Two reflections in a row ★★★
The point (−3, 4) is reflected across the x-axis, and the result is reflected across the y-axis. Find the final point.
Problem 10 Finding missing coordinates ★★★
- The point (3, y) is the reflection of (3, −8) across the x-axis. Find y.
- The point (x, 2) is the reflection of (−5, 2) across the y-axis. Find x.
Problem 11 Rectangle side lengths ★★★
Rectangle ABCD has the vertices shown. Find the length of each side and the perimeter.
Problem 12 Right triangle legs ★★★
Find the lengths of the vertical and horizontal sides of the triangle.
Problem 13 Trail map ★★★
A trail starts at (−5, −2) and runs straight east to a campsite at (3, −2). How long is the trail if each unit is 1 mile?
Problem 14 Reflections across the y-axis ★★★
Which pairs are reflections of each other across the y-axis? (a) (3, −5) and (−3, −5) (b) (2, 4) and (−2, −4) (c) (−6, 0) and (6, 0)
Problem 15 Park walk ★★★
On the park map, a walker goes from the library straight to the pool, then straight to the cafe. How many blocks does she walk in all?
Problem 16 Rectangle perimeter and area ★★★
A rectangle has vertices A(−5, 1), B(2, 1), C(2, −4) and D(−5, −4). Find its side lengths, perimeter and area.
Problem 17 Square garden ★★★
Three vertices of a square garden are (−2, −2), (4, −2) and (4, 4). Find the fourth vertex, the side length, and the vertices of the garden’s reflection across the y-axis.
Problem 18 Parallelogram heights ★★★
A parallelogram has vertices (−6, 2), (−1, 2), (1, −2) and (−4, −2). Find the length of each horizontal side and the vertical distance between them.
Problem 19 Reflecting a triangle ★★★
Triangle PQR has vertices P(1, 2), Q(4, 2) and R(4, 6). Reflect it across the y-axis and name the new vertices. Do any side lengths change? Explain.
Problem 20 Explain the error ★★★
Marcus says (−4, 0) is in Quadrant II. Explain his mistake, then give one point in Quadrant II with y-coordinate 7.
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