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The Case of the Missing Coordinates

6th Grade AZ Math Standard

S4C3-PO2Carol Cherry/MPS/2010

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Just the Facts

To help you solve the case, we’ll

review some basic facts about

coordinates in the next few slides.

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Ordered PairsAlways start at the origin (0,0)

The first number tells how many units to go on the horizontal, or x-axis.

If the first number is positive, e.g. (3,4), go Right 3 units

If the first number is negative, e.g. (-3,4) go Left 3 units

€

y

€

x

€

(0, 0)

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+

€

–

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The second number tells how many units to go on the vertical, or y-axis.

If the second number is positive, e.g. (3,4), go Up 4 units

If the second number is negative, e.g. (3,-4), go Down 4 units

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y

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x

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(0, 0)

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+

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–

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To solve the mystery of the missing coordinates you need

to know the properties of some important polygons

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Clues that a polygon is a square

Number of sides: 4

Number of pairs of parallel sides: 2

Number of right angles: 4

Number of congruent sides: 4

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Clues that a polygon is a rectangle

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Number of pairs of parallel sides: 2

Number of right angles: 4

Number of congruent sides: 2 pairs of opposite sidescongruent

Number of sides:

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Clues that a polygon is a parallelogram

Number of sides: 4

Number of pairs of parallel sides: 2

Number of right angles: 0

Number of congruent sides: 2 pairsopposite sidescongruent

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Clues that a polygon is an isosceles trapezoid

Number of sides: 4

Number of pairs of parallel sides: 1

Number of right angles: 0

Number of congruent sides: One pair of opposite sides congruent

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Here is an example of how a great detective would solve this case.

Goal:Find the missing coordinates of this parallelogram and justify your answer.

Properties to use as clues:Both pairs of sides are parallel, so the bottom line, or base, has to be parallel to the top line. That means the vertex will be on the same line as the vertex at (-6,1) so 1 is the second coordinate.The base has to be congruent to the top line, which is 6 units long. So start at the left vertex, -6, and go 6 units right. The X, or first coordinate is at X=0.

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y

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x

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(−6,1)

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(−4,6)

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(2,6)

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(0,1)

The missing coordinates are (0,1)

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Now you’re ready to find some missing coordinates!

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What are the missing coordinates

of this square?

The coordinates are:

(-1,-1)

Explain how you found them.

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y

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x

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(−1,5)

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(5,5)

1)- (5,

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Find the coordinates for the

fourth vertex of this rectangle.

Ordered pair:

(-6,4)

Explain how you found them.

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y

€

x

€

(−6,−4)

(4,4)

€

(4,−4)

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Locate the missing coordinates in this

parallelogram

See the next slide for a tip

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y

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x

€

(-4,2)

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(-1,7)

€

(3,2)

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Think of the parallelogram as a rectangle and

2 triangles

The triangles are congruent.

The left triangle has a base of 3 units.

Therefore, the base of the triangle on the right is 3 units.

Now you can find the missing coordinates: (6,7)

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y

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x

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(-4,2)

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(-1,7)

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(3,2)

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← 3 →

€

← 3 →

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Find the coordinates for the missing vertex of this parallelogram.

Coordinates:

(5,-2)

Justify your answer.

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y

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x

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(-5, -8)

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(-3, -2)

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(3, -8)

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Think of this isosceles trapezoid as a square

plus 2 triangles.

Missing Coordinates:

(5,-1)

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y

€

x

€

(−6,−1)

€

(−3,4)

€

(2,4)

Find the missing coordinates.

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One last chance to practice:Find the ordered pair for the missing vertex in this parallelogram.

Tell your partner which properties of a parallelogram helped you find your answer.

Ordered pair for the missing vertex:

(4,7)

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y

€

x

€

(−6,2)

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(1,2)

€

(−3,7)

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For more practice with ordered pairs, try these websites:

http://www.oswego.org/ocsd-web/games/BillyBug2/bug2.html

http://www.shodor.org/interactivate/activities/MazeGame/

http://funbasedlearning.com/algebra/graphing/default.htm

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Thank you for

helping solve the

Case of the Missing

Coordinates. Now

you are ready to

solve your own

cases.