TVwo §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) !

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!).

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.