1TH/Vwo §3.1 + §3.2 + §3.3

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 1

§3.1 + §3.2 + §3.3

Explanation + TASK  for finding coordinates

of a point on a line:

EXPLANATION:

we have a coordinate system with 

+ an x-axis as horizontal axis

+ a y-axis as vertical axis

TASK:   FILL IN the COORDINATES IN NEXT SLIDE:

 a line through (.., ..) and (.., ..), the

    two points given by dots.

TASK 1
The points are:

1. (0, 6) and (18, 10)
2. (6, 0) and (10, 18)
3. (0, 6) and (10, 18)
4. (6, 0) and (18, 10)

Explanation finding coordinates

of a point on a line:

Answers:

We always write the horizontal coordinate first

and then vertical one. Use brackets and a comma!

So:  (0, 6) and (10, 18)

Suppose we want to find the coordinates for A and B...

There's a slight problem:

The points A and B are no grid points!

Therefore you cannot read off their 

coordinates. How sad...

However the next slide offers us a solution!

In order to find the coordinates of A and B ...

Let's use GRID POINTS C and D first! As follows:

Going from C to D means:

+ going 5 grids to the right and

+ going up 20 grids

+ in order to find coordinates of point A we do:

   going 1 to the right, which means going up 4

+ so we get:    A(1, 9)   

    9  we got by doing:   5 + 4 = 9

Explanation finding coordinates point A by a 

RATIO TABLE (=verhoudingstabel):

See from the table:

+ going 5 grids to the right means

+ going 20 grids up

+ so going 1 grids to the right means

+ going up 20 : 5 = 4 grids up

TASK 2  for you:

 find the coordinates for B!   

(WORK IT OUT, not just the answer!)

Take these steps now:

1. open Notebook

2. get a pen, pencil and a geo

3. work out coordinates of point B!

B's coordinates are:

1. (4, 22)
2. (21, 4)
3. (22, 4)
4. (4, 21)

SOLUTION TASK 2,      for:

 finding the coordinates for POINT B:

Again we start from point  C !

From C to B means going 4 grids to the right.

We now know that going 1 grid to the right means

going 4 grids up.

So we have to go up:   4 x 4 = 16 grids.

C lies at a height of 5 grids. So the y-coordinate 

of B is 5 + 16 = 21.   Point B is  (4, 21)

Task 3, for you!

Find the coordinates 

for point F.

First COPY the PICTURE on the right.

Use the GRID POINTS

that are on the line!

Again: WORK IT OUT!

Only then you learn a lot.

Task 3:
The coordinates of F are:

1. (1, 43)
2. (1, 42)
3. (43, 1)
4. (42, 1)

Explanation Task 3:

Watch the 2 GRID POINTS, at the 

start and at the end of the line segment.

+ going 5 grids to the right means

+ going down 15 grids, so

+ going to the right 1 grid, means

+ going down 15 : 5 = 3 grids.

+ so the y coordinate of F is 45 - 3 = 42 and

+ point F has coordinates:    (1, 42)

Task 4 for you:

Find the coordinates for point G.

Again work it all out!

1. (34, 3)
2. (3, 34)
3. (36, 3)
4. (3, 36)

Explanation task 4:

In the RATIO TABLE (verhoudingstabel)

you see that

+ going 5 grids to the right means

+ going down 15 grids

+ so: going to the right 1 grid means

+ going down 3 grids and 

+ going to the right 3 grids means

+ going down 3 x 3 = 9 grids.

So the 2nd coordinate of G is 45 - 9 = 36.

So we get:              G (3, 36) !

If you want a break with an exciting story, then raise your hand!

(Remember, yesterday was Halloween!)

After this scary break in good German...

some more questions for you about:

§4.1,   §4.2  and  §4.3 !

Variables are: euros and km,
units are money and length.

1. True
2. False
3. The other way around.

'Join the points' means in our maths lessons ....

a. have a get together with the points 

b. draw a line through the given points

     c. both can be correct but b is more likely

Answer on next slide!

'Join the points' means ...

1. get together with the points
2. draw a line through the points
3. both correct; B more likely

The point A(3, 8) lies to the left of
B(6, 7)

1. True
2. False

Explanation:

A(3, 8) lies to the left of B(6, 7), because the 1st coordinate of  A is smaller then the 1st coordinate of B.

If still not clear, watch the SKETCH on the next slide (that you could make too!).

Graf Zeppelin was ...

1. the namegiver of the GRAPH
2. the inventor of the Zeppelin
3. was an aircraft carrier (=vliegdekschip) of the Germans during WW 2.
4. a cousin of Count von Count in Sesamestreet

A smooth line ....

1. is online most of the time.
2. is a straight line.
3. has no sudden changes.
4. does not have sharp turns.

Homework :

Make 28 + 29 from §4.5 already.

This saves you some work, when we do §4.5, tomorrow!

Remember to DRAW the GRAPHS with PENCIL + GEO !