# Cartesian Coordinates in 2 Dimensions - Level 2

Definition: The Cartesian Coordinate System is the rectangular system of locating points in the plane.

Rule: A point (x,y) is located by finding its horizontal x-coordinate and its vertical y-coordinate.

Interactivity 1    Interactivity 2    Interactivity 3    Interactivity 4

 1. Click on the point icon . In the drawing pad, find the point with coordinates (1,1) and then click. Point A should be drawn. Check the coordinates of point A by rolling your mouse over it. 2. Find the coordinates and draw the point B(1,4). Is B above or right of A?   3. Find the coordinates and draw the points C(5,4) and D(5,1). 4. Use the segment tool and make the rectangle ABCD. 5. What is the length and height of the rectangle ABCD?
 1. Click on the Reset icon to clear the drawing pad. 2. Find and draw the points A(5,0), B(1,3) and C(1,0) 3. Use the segment tool to make the triangle ABC. What kind of triangle is ΔABC?   4. From the coordinates, can you find the lengths of \overline {CA} and \overline {CB} ?   5. Using Pythagoras' theorem, what is the length of \overline {AB} ?     To check your work, click on View -> Algebra Window.
 1. Click on the Reset icon to clear the drawing pad. 2. Click on the Move Drawing Pad icon and then click and drag on (0,0) to put it in the middle of the drawing pad. 3. Find and draw the points A(-2,-1), B(1,-4) and C(1,1) 4. Use the segment tool to make the triangle ABC. 5. Click on View -> Algebra Window. You should see 3 free points and 3 dependent line segments: a, b and c. 6. Click on the Move icon and click and drag C until ABC is an isosceles triangle. Answers: Isosceles triangle means 2 equal sides so we want two of a, b or c to be the same. Try C=(0,2). Can you find another point? (There are many, many points.)  Another point:
 To clear the drawing pad, click on the button. 1a. Draw A(0,3) and B(4,1). b. Find a point C (there are 2!) to make triangle ABC a right-triangle   c. Connect A, B and C with line segments. d. Use Pythagoras' theorem to check that \overline {AB} is the "correct" length! 2a. Clear your drawing pad. b. Draw A(1,1) and B(4,3). c. Determine and draw the points C and D that make ACBD a rectangle.
 Examples                          (x,y)=(horizontal,vertical) (Remember: in English "h" is before "v"). Possible continuations: Quadrant 1: Higher or wider? Quadrant 1: Points - Find their coordinates Quadrant 1: Making dynamic right-triangles using x(A) and y(B); dynamic rectangles... Quadrants 4:  What quadrants? Quadrants 4: Points - Find their coordinates

Related Topics

(:commentbox:)