Challenges

1.  Construct A, B and C so that A is 3 inches from B and B is 2 inches from C.  Display distances and hide any unnecessary objects. 

Bring up a new sketch.  Plot a point and label it A.  Under the edit menu, choose preferences and change units to inches.  Select point A and under the transform menu choose translate.  Put in 3 inches and 0 degrees. Label the new point B.  Repeat the process creating a new point 2 inches from B. Choose point A then B with the select tool (arrow) and under the measure menu select distance.  Repeat this for BC

2.  Construct the perpendicular bisector of a segment labeling the segments endpoint A and B and its midpoint M.  Label the perpendicular bisector t.  Place point P on the perpendicular bisector.  Find the distance from P to A and P to B and the distance from A to M an B to M.

Bring up a new sketch.  Using your segment tool draw a segment and label the endpoints A and B.  If the point labels have not come up automatically you may want to change your preferences under the edit menu to include show labels for points.  If they have not come up use the alphabet key and click on the endpoints.  A capital letter should appear.  If the letters are not A and B double click on the letter and a text area should come up in which you can change the label. Select the segment using your arrow tool and choose under the construct menu - midpoint.  You can also get the midpoint by pressing the control key and the M key at the same time. Using your arrow tool (select tool)  select the segment and midpoint (not endpoints) and under the construct menu, choose perpendicular bisector.  Using your alphabet (A) tool click on the perpendicular line.  A lower case label should appear.  Double click with the A tool on this and change the label to t.  Using the point tool place a point on the perpendicular bisector and label it P.  Find the distance form P to A and P to B using the same process from Challenge I.  Repeat to find the measures of AM and MB.

3.  Construct two concentric circles so the radius of one is exactly twice the radius of the other.  Also construct a point P so that when it is dragged the size of the circles change but the ratio remains 2:1.  Display the radius lengths of the two circles and use the calculator to display the ratio of the larger circle to the smaller. 

Use the circle tool and construct a circle.  Re- label the point on the circle P.  Select the center of the circle and point on the circle and under measure choose distance to find the length of the radius.  Select the length of the radius (box in upper left corner) and under the measure menu, choose calculator.  In the calculator choose 2  times (*) and in the value box choose the radius.  OK this and this should appear as a box in the upper left of your screen.  Select the center of your circle ( arrow key) and the value box of 2 times the radius.  Under the construct menu choose circle by center and radius.  A concentric circle twice as big should appear. To find its radius, make sure nothing else is selected.  Click on the circle and under the measure menu ask for the radius.  Select both the larger circle's radius measure and the smaller circles radius measure.  Under measure, select calculator and in the value box, choose the larger radius then the division operation followed by the smaller radius value.  The ratio of the radii should appear. 

4.  Construct a circle with two points  A and B diametrically opposed so that when A is dragged, B remains diametrically opposite it. 

Using the circle tool, construct a circle.   Place a point on the radius and label the point A.  Double click on the center of the circle or choose the center and under the transform menu choose mark center.  With A selected  choose rotate under the transform menu and rotate the point 180 degrees. Label this new point B. 

5.  Construct a point labeled A on a line labeled m.  Now construct two more points so that the distance from B to A is always three times the distance from B to C .  When A, B or C are are dragged the distances should change, but the three to one ratio must remain.  Display the distances and use the calculator to display the three to one ratio. 

Use the line tool to draw a line.  Two points should be on the line label them A and B.  Double click on point B and then select A. Under the transform menu choose dilate and make a ratio of 1 to 3.  A point should appear between A and B one third of the distance from B to A.  Label this point B.  Choose point A then point B and under the measure menu choose distance.  Repeat the process for BC.  Choosing the two displayed lengths go to measure calculate and under values select AB then divide by and choose BC under values.  

6. Challenge 6 Construct a non-square quadrilateral with four sides of length eight centimeters.  Side lengths should remain eight centimeters when any object on the screen is dragged.  Display the side lengths. 

Use your point tool and place a point on your sketch.  With the point selected, choose translate under the transform menu and translate the point 8 cm at 0 degrees. Draw a segment to connect the two points.  Label the endpoints A and B.  Choose point A and the segment AB and under construct  choose circle by center and radius.  Then put a point on this circle above the segment and label the point C. Draw in the radius from A to C.  Choose point C and radius AC and construct another circle by center and radius.  Repeat the process choosing point B and the radius AB.  Where the circle B and circle C intersect above the segment, place a point at the intersection.  Label this point D and draw in segments BD and CD.  Display the lengths of AB, DB, CD and AC and hide the circles. (control H)

7.  Construct a rectangle whose height is exactly twice its width.  When a vertex is dragged the rectangles sides must change length but the height must remain twice the base.  Hide any unnecessary objects and display the height to the width without using the calculator. 

Construct a horizontal segment and label the endpoints A and B.  Double Click on A (mark as center of rotation).  Select point B and under transform choose rotate 90 degrees.  Double click on this new point (relabel as M), select point A and rotate under the transform menu 180 degrees.  Label this new point D.  Connect A to point D with your segment tool.  Double click on point   D and choose M.  Rotate M  90 degrees and label this new point C.  Connect with the segment tool from D to C and from B to C.  Hide point M.  Click on segment AD and then on segment AB.  Choose ratio under the measure menu.

Construct a triangle with side lengths of exactly 3, 4 and 5 inches.  Side lengths must remain 3, 4 and 5 when any object on the screen is dragged.  Display the side lengths and hide any unnecessary objects. 

Under the display menu choose preferences and change to inches. Using your point tool place point A on the screen in the upper left.  Translate this point 5 inches to the left ( 0 degrees) .  Connect with your segment tool.  Place another point in the upper left and translate using the same method, 4 inches. Connect with segment tool.  Repeat with a third point and translate 3 inches. Place a point lower on your screen.  Label the point D. Choose point D and the 5 inch segment and construct a circle by center and radius under the construct menu.  Draw in a radius and label the point on the circle E.  Choose point D and  the 4 inch segment and under construct - circle by center and radius.  Choose point E and the three inch segment and under construct, circle by center and radius.  These two circles should intersect in two places.  Put  a point at one of the intersections of the circles and label the point F.  Connect from D to F and from C to F with your segment tool.  Hide the circles and the original segments of lengths 3,4,5.  Click on the three sides of your triangle and get the lengths of each under the measure menu. 

9.  Construct a circle with two points on it.  A and B.  When A is moved around the circle, point B must travel around it too, but twice as fast.  That is for every one time that A rotates around the circle, B must rotate two times.  Hide any unnecessary objects. 

Draw a circle and hide the center and point on the circle.  Place another point on the circle and label the point A. With A selected chose Action Button  from the edit menu, then animation.  In the gray menu choose under speed other and select 1.  Put another point on the circle.  Repeat the animation process but change the speed to 2.  Check to make sure that when your animation buttons are chosen that point B laps point A at the half way mark.

10.  Construct any object composed of points lines and circles with an animate button that slides it back and forth along a line. The car shown is a simple object, but make yours something more creative.  Note that when any piece of your construction is dragged, the object must not lose its shape. 

Example. Sketch
This sketch shows how you can animate a circle along the line.  First draw a line.  Then place a point on the line.  Animate the point by selecting the point and under edit choose action button and choose animation. Animate the point bidirectionally along the line.  Choose the point and the line and construct a perpendicular.  Then choose the point on the line and translate the point 1 cm.  Choose the new point on the perpendicular then the point you put on the line and under construct. Construct a circle by center and point.  When you press the action button the circle should travel back and forth.  Remember that when you make attach anything else it must be so that it holds so connect it to either the original point or the translated point by a transformation so that it holds.  Sketch 2

Challenge 10 - Check out this website for other students animations   http://www.sad1.k12.me.us/pihs/math/sketchpad.htm