Geogebra . . .once again !

Geogebra . . .once again !

Season 1

Episode AP06 Document 1 period

In the gure below,

ABCD

^{is asquare and itsside measures 20m.}

M

^{is amoving point}

on the segment

AB

^.

AM N P

^{is a square too.}

The aim of this session is to nd the position of the point

M

^{for whih}

AM P N

^and

△ DN C

^{havethe same area.}

D C

B A

P N

× M

Part A – Using Geogebra

1. Use Geogebra todraw the gure. When it'sdone, allyour teaher who willhek

your gure.

2. Move the point

M

^on

AB

^{and onjeture thepositionof}

M

^{for whih the areasare}

equal.

Part B – Using function graphs

Let

x

^{represent the lengthof}

AM

^.

1. What is the minimal value for

x

^{.Explain quikly your answer.}

2. What is the maximal value for

x

^{. Explain quikly your answer.}

3. Let

f

^{bethe funtion thatmaps any adequatevalueof}

x

^tothe orrespondingarea of

AM N P

^{. Give the expression of}

f(x)

^.

4. Let

g

^{be the funtion that mapsany adequate value of}

x

^{to the} orrespondingarea of

△ DN C

^{. Give the expression of}

g(x)

^.

5. Usinggeogebra,drawthe graphof

f

^{,then thegraph of}

g

^{.When it'sdone,allyour}

teaher who willhek your gure.

6. Dedue from the urve, the position of the point

M

^{for whih the two areas are}

equal.

Part C – Using computation

1. Solve the equation

( x + 20)( x − 10) = 0

^.

2. Expand the expression

( x + 20)( x − 10)

^.

3. Use the two previous questions and the expressions of

f

^and

g

^{to nd the value of}

x

^{for whih the two areasare equal.}

Geogebra . . .once again !

Season 1

Episode AP06 Document 1 period

In the gure below,

ABCD

^{is asquare and itsside measures 20m.}

M

^{is amoving point}

on the segment

AB

^.

AM N P

^{is a square too.}

The aim of this session is to nd the position of the point

M

^{for whih}

AM P N

^and

△ DN C

^{havethe same area.}

D C

B A

P N

× M

Part A – Using Geogebra

1. Use Geogebra to draw the gure.

2. Move the point

M

^on

AB

^{and onjeture thepositionof}

M

^{for whih the areasare}

equal.

Part B – Using function graphs

Let

x

^{represent the lengthof}

AM

^.

1. What is the minimal value for

x

^{.Explain quikly your answer.}

2. What is the maximal value for

x

^{. Explain quikly your answer.}

3. Let

f

^{bethe funtion thatmaps any adequatevalueof}

x

^tothe orrespondingarea of

AM N P

^{. Give the expression of}

f ( x )

^.

4. Let

g

^{be the funtion that mapsany adequate value of}

x

^{to the} orrespondingarea of

△ DN C

^{. Give the expression of}

g(x)

^.

5. Using geogebra, draw the graph of

f

^{, then the graph of}

g

^.

6. Dedue from the urve, the position of the point

M

^{for whih the two areas are}

equal.

Part C – Using computation

1. Solve the equation

(x + 20)(x − 10) = 0

^.

2. Expand the expression

( x + 20)( x − 10)

^.

3. Use the two previous questions and the expressions of

f

^and

g

^{to nd the value of}

x

^{for whih the two areasare equal.}