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Draw Polygons in the Coordinate Plane Given Coordinates for the Vertices

For each problem involving a coordinate plane, draw the polygon first. Use absolute value to find horizontal and vertical side lengths. Include units in perimeter answers.

Grade 6·22 problems·~35 min·Common Core Math - Grade 6·standard·6-g-a-3

Work through problems with immediate feedback

Recall / Warm-Up

In which quadrant does the point $(-3, 5)$ lie?

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

What is $|-7 - 3|$ ?

-10

-4

Two points lie on the same horizontal line: $A(-4, 2)$ and $B(5, 2)$ . What is the distance between them?

Fluency Practice

$Coordinate plane showing rectangle with vertices A(-3,2), B(4,2), C(4,-1), D(-3,-1) plotted and connected.$

Vertices $A(−3, 2)$ , $B(4, 2)$ , $C(4, −1)$ , $D(−3, −1)$ form a rectangle.
Vertex $A$ is in Quadrant ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .
Vertex $C$ is in Quadrant ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .
Side $AB$ is a ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ segment (horizontal or vertical).
Side $BC$ is a ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ segment.

quadrant of A:

quadrant of C:

type of AB:

type of BC:

A right triangle has vertices at $P(-2, 4)$ , $Q(-2, -3)$ , and $R(5, -3)$ . Which sides can have their length found using the absolute value of coordinate differences?

Only side PQ

Only side QR

Sides PQ and QR only

All three sides

$Coordinate plane showing vertical segment PQ with P at (-2, 4) and Q at (-2, -3), with unknown length marked.$

Find the length of segment $PQ$ with $P(-2, 4)$ and $Q(-2, -3)$ .

Find the length of segment $QR$ with $Q(-2, -3)$ and $R(5, -3)$ .

What is the length of the side connecting $M(2, 5)$ and $N(6, 2)$ ? (Use only Grade 6 methods.)

4 units (use $|x_M - x_N|$ )

3 units (use $|y_M - y_N|$ )

7 units (add $|x_M - x_N| + |y_M - y_N|$ )

The length cannot be found using the absolute value method — the segment is diagonal.

Varied Practice

Vertices are given in order: $A(1, 4)$ , $B(5, 4)$ , $C(5, 1)$ , $D(1, 1)$ . What shape is formed when the vertices are connected in order ( $A \to B \to C \to D \to A$ )?

A triangle

A rectangle

A triangle (if D is connected to B, not A)

An open figure (the polygon is not closed)

Rectangle $ABCD$ has vertices $A(-3, 2)$ , $B(4, 2)$ , $C(4, -1)$ , $D(-3, -1)$ .
Find the length of side $AB$ .

Two vertices of a polygon are $E(-1, 3)$ and $F(4, 3)$ . What is the length of segment $EF$ ?

3 units

4 units

5 units

Cannot be determined — the segment is diagonal.

$Coordinate plane showing rectangle ABCD with vertices A(-3,2), B(4,2), C(4,-1), D(-3,-1). Each side has an unknown length marked.$

Rectangle $ABCD$ has vertices $A(-3, 2)$ , $B(4, 2)$ , $C(4, -1)$ , $D(-3, -1)$ .
Find the length of side $AB$ : ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ units.
Find the length of side $BC$ : ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ units.
Find the perimeter of the rectangle: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ units.

AB length:

BC length:

perimeter:

A rectangle has vertices at $(0, 0)$ , $(8, 0)$ , $(8, 5)$ , and $(0, 5)$ . What is the perimeter of the rectangle?

Word Problems

A park has boundary vertices at $P(-4, 3)$ , $Q(2, 3)$ , $R(2, -2)$ , and $S(-4, -2)$ . Each unit represents 1 meter.

What shape is the park boundary?

A triangle

A rectangle

A trapezoid

A pentagon

What is the perimeter of the park in meters?

A right triangle has vertices at $T(0, 0)$ , $U(9, 0)$ , and $V(9, 12)$ . Each unit represents 1 foot.

What is the sum of the two legs (non-hypotenuse sides) of the triangle in feet?

$Coordinate plane showing L-shaped garden with vertices A(-3,4), B(3,4), C(3,1), D(1,1), E(1,-2), F(-3,-2) connected in order.$

A community garden has an L-shaped boundary with vertices (in order): $A(-3, 4)$ , $B(3, 4)$ , $C(3, 1)$ , $D(1, 1)$ , $E(1, -2)$ , $F(-3, -2)$ . All sides are horizontal or vertical. Each unit = 1 meter.

What is the perimeter of the L-shaped garden in meters?

A rectangular swimming pool has vertices at $(−5, 4)$ , $(7, 4)$ , $(7, −3)$ , and $(−5, −3)$ . Each unit represents 1 yard. Fencing costs $12 per yard.

What is the total cost to fence the perimeter of the pool?

Error Analysis

Jada connects the vertices $A(1, 3)$ , $B(5, 3)$ , $C(5, -1)$ , $D(1, -1)$ in this order: $A \to C \to B \to D \to A$ .

What error did Jada make, and what shape should have been formed?

Jada connected the vertices out of order. Following the given order $A \to B \to C \to D \to A$ creates a rectangle.

Jada made no error. Any connection order gives the same polygon.

Jada should not have connected back to $A$ at the end.

The vertices cannot form a rectangle.

Marco needs the length of segment from $P(2, 1)$ to $Q(6, 4)$ . He computes:
Length $= |2 - 6| = |-4| = 4$ units

What error did Marco make?

Marco computed the correct length.

Marco found the horizontal distance, but the segment $PQ$ is diagonal — its length cannot be found using absolute value of x-coordinates alone.

Marco should have used $|y_P - y_Q| = |1 - 4| = 3$ units instead.

Marco should have added the x-coordinates: $2 + 6 = 8$ units.

Challenge / Extension

A rectangle has three of its four vertices at $(−2, 5)$ , $(6, 5)$ , and $(6, −3)$ . What are the coordinates of the fourth vertex? What is the perimeter of the rectangle?

A polygon has vertices at $(0, 0)$ , $(4, 0)$ , $(4, 3)$ , and $(0, 3)$ .
Width: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲
Height: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲
Area: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲

width:

height:

area:

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