Presentation on theme: "The Case of the Missing Coordinates"— Presentation transcript:
1The Case of the Missing Coordinates 6th Grade AZ Math StandardS4C3-PO2Carol Cherry/MPS/2010
2Just the FactsTo help you solve the case, we’ll review some basic facts about coordinates in the next few slides.
3Ordered Pairs Right 3 units Left 3 units Always 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), goRight 3 unitsIf the first number is negative, e.g. (-3,4) goLeft 3 units
4The second number tells how many units to go on the vertical, or y-axis. If the second number is positive, e.g. (3,4), goUp 4 unitsIf the second number is negative, e.g. (3,-4), goDown 4 units
5To solve the mystery of the missing coordinates you need to know the properties of some important polygons
6Clues that a polygon is a square Number of sides:4Number of pairs of parallel sides:2Number of right angles:4Number of congruent sides:4
7Clues that a polygon is a rectangle Number of sides:4Number of pairs of parallel sides:2Number of right angles:4Number of congruent sides:2 pairs of opposite sidescongruent
8Clues that a polygon is a parallelogram Number of sides:4Number of pairs of parallel sides:2Number of right angles:Number of congruent sides:2 pairsopposite sidescongruent
9Clues that a polygon is an isosceles trapezoid Number of sides:4Number of pairs of parallel sides:1Number of right angles:Number of congruent sides:One pair of opposite sides congruent
10Here 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.The missing coordinates are (0,1)
11Now you’re ready to find some missing coordinates!
12What are the missing coordinates of this square? The coordinates are:(-1,-1)Explain how you found them.
13Find the coordinates for the fourth vertex of this rectangle. Ordered pair:(-6,4)Explain how you found them.
14Locate the missing coordinates in this parallelogram See the next slide for a tip
15Think 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)
16Find the coordinates for the missing vertex of this parallelogram. (5,-2)Justify your answer.
17Think of this isosceles trapezoid as a square plus 2 triangles. Find the missing coordinates.Missing Coordinates:(5,-1)
18One 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)
19For more practice with ordered pairs, try these websites:
20Thank you for helping solve the Case of the Missing Coordinates Thank you for helping solve the Case of the Missing Coordinates. Now you are ready to solve your own cases.