Learning Goal: Plot polygon vertices on the coordinate plane and find side lengths when points share an x- or y-value.
Vocabulary
coordinate planeA grid made by a horizontal x-axis and a vertical y-axis crossing at the origin (0, 0).
ordered pairTwo numbers (x, y) that name a point's location: x tells left/right, y tells up/down.
vertexA corner point of a polygon where two sides meet (plural: vertices).
polygonA closed 2D shape with straight sides, such as a triangle, rectangle, or pentagon.
What You Need to Know
A point (x, y) is found by moving x units left/right from the origin, then y units up/down.
If two points share the same y-value, the side is horizontal; its length = the difference of the x-values.
If two points share the same x-value, the side is vertical; its length = the difference of the y-values.
To find a length, subtract the smaller coordinate from the larger one (or count grid units between them).
When points are on opposite sides of 0, the distance is the sum of the absolute values (from −3 to 7 is 10 units).
Add up the side lengths to find the perimeter of a polygon.
Worked Example I Do — watch how it works
A rectangle has vertices A(−3, 2), B(7, 2), C(7, −1), and D(−3, −1). Find the length of side AB and side BC.
Step 1. AB: A and B share y = 2, so it is horizontal. Length = 7 − (−3) = 10 units.
Step 2. BC: B and C share x = 7, so it is vertical. Length = 2 − (−1) = 3 units.
Step 3. So AB = 10 units and BC = 3 units.
Answer: AB = 10 units, BC = 3 units
Guided Practice We Do — try it together
1. Points P(2, 5) and Q(2, 1) are two vertices of a polygon. How long is side PQ?
💡 Hint: Same x-value means a vertical side; subtract the y-values.
2. Points M(−4, 3) and N(6, 3) are connected. How long is side MN?
💡 Hint: Same y-value; the points are on opposite sides of 0, so add 4 + 6.
3. A square has vertices (1, 1), (1, 6), (6, 6), and (6, 1). What is the length of one side?
💡 Hint: Pick two vertices that share an x- or y-value and find the difference.
Independent Practice You Do — show your work
1. Find the length of the side joining (3, 8) and (3, 2).
2. Find the length of the side joining (−5, 4) and (4, 4).
3. A rectangle has vertices (−2, 5), (6, 5), (6, −3), and (−2, −3). Find its length and width.
4. Find the perimeter of a rectangle with vertices (0, 0), (9, 0), (9, 4), and (0, 4).
5. Points (−6, −2) and (5, −2) are two vertices. How far apart are they?
MCAP-Style Practice
Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.G.A.3.
Item 1Selected Response6.G.A.3
A side of a polygon connects the points (−4, 1) and (8, 1). What is the length of this side?
Select the correct answer.
Item 2Selected Response6.G.A.3
A rectangle has vertices (2, 7), (2, −1), (5, −1), and (5, 7). What is its perimeter?
Select the correct answer.
Item 3Constructed Response6.G.A.3
A triangle has vertices A(1, 2), B(1, 9), and C(6, 2). Find the length of vertical side AB and horizontal side AC.
Enter your answer in the space provided. Show your work.
Enter your answer:
Teacher Answer Key (click to show)
Independent 1
6 units
Independent 2
9 units
Independent 3
8 units by 8 units (it is a square)
Independent 4
26 units
Independent 5
11 units
Item 1 · 6.G.A.3
C — Same y-value, so it is horizontal. From −4 to 8 is 8 − (−4) = 12 units.