Need help with Maths questions(o level).

[musiclover gurl]

Each interior angle of a regular polygon is p times each exterior angle.
Find an expression, in terms of p, for
(a) An exterior angle. [1]
(b) The number of sides of the polygon. [1]



The diagram shows triangles A, B and C.
(a) Triangle A is mapped onto triangle B by an anticlockwise rotation.
(i) Write down the angle of rotation. [1]
(ii) Find the coordinates of the centre of rotation. [1]

(b) Triangle A is mapped onto triangle C by a stretch.
(i) Write down the scale factor. [1]
(ii) Write down the equation of the invariant line. [1]


There are two questions. I am unable to work the second parts of both question though they are simple..I wonder why. Can someone help me wiz this, plz?
They are questions from Maths 2011 Paper 1

 

[Dark Destination]

1a) 180/(p-1) ?

 

[musiclover gurl]

1a) 180/(p-1) ?

Yess.
But the second part is the real trouble

 

[Dark Destination]

Yess.
But the second part is the real trouble

Exterior angle = 360/n

Equate this to the other expression for exterior angle found in first part, and make n the subject?

 

[musiclover gurl]

Exterior angle = 360/n

Equate this to the other expression for exterior angle found in first part, and make n the subject?

yaaaa. Thanks. I actually forgot that the sum of the exterior angle of a polygon adds up to 360. Uhmm, if u don't mind can also plz help me wiz the other question? Only if u wish to.

 

[Dark Destination]

yaaaa. Thanks. I actually forgot that the sum of the exterior angle of a polygon adds up to 360. Uhmm, if u don't mind can also plz help me wiz the other question? Only if u wish to.

Scale factor is 2. Invariant line is x = -1

To find the scale factor of stretch, you have to look at the side of the shape which increases in size.

The side on the line y=3 increases in size. As you can see, it doubles. So from that we know that scale factor is 2.

To find invariant line, you have to visualize the shape and look at its distances. It's not the y-axis because distance of (1,3) is 1, while distance of (3,3) is 3, that can only happen if scale factor is 3. But it's 2.

But if you check it with x = -1, you can see that the distance of each point on C, is double the distance of the corresponding point on A from the invariant line, because the stretch factor is 2.

This is hard to explain. Tell me if you are still confused about something.

 

[musiclover gurl]

Scale factor is 2. Invariant line is x = -1

To find the scale factor of stretch, you have to look at the side of the shape which increases in size.

The side on the line y=3 increases in size. As you can see, it doubles. So from that we know that scale factor is 2.

To find invariant line, you have to visualize the shape and look at its distances. It's not the y-axis because distance of (1,3) is 1, while distance of (3,3) is 3, that can only happen if scale factor is 3. But it's 2.

But if you check it with x = -1, you can see that the distance of each point on C, is double the distance of the corresponding point on A from the invariant line, because the stretch factor is 2.

This is hard to explain. Tell me if you are still confused about something.

I still did not understand but never mind I wll find another way of tackling such questions. ThanksSSS AAA LOOOT for the help.

 

[Dark Destination]

I still did not understand but never mind I wll find another way of tackling such questions. ThanksSSS AAA LOOOT for the help.

Basically, you should understand what STRETCH really is. Only then you'll be able to understand how to find out the invariant line and the scale factor.

The invariant line is the line from which the object is stretched. For example, the distance of a point from invariant line is 2. If you want to stretch it with a scale factor of like 4, you will multiply 2 with 4, and place the image 8 boxes from the invariant line.

The invariant line is found out through observing the diagram. Mostly it's the y-axis, but sometimes as you see it can be x = -1 or x = -2.

If the invariant line is vertical, then the object moves or is stretched horizontally. But if the invariant line is horizontal (in some cases it is the x-axis). then the stretch is done vertically. The image will be vertically above the object.

 

[musiclover gurl]

View attachment 48360

Basically, you should understand what STRETCH really is. Only then you'll be able to understand how to find out the invariant line and the scale factor.

The invariant line is the line from which the object is stretched. For example, the distance of a point from invariant line is 2. If you want to stretch it with a scale factor of like 4, you will multiply 2 with 4, and place the image 8 boxes from the invariant line.

The invariant line is found out through observing the diagram. Mostly it's the y-axis, but sometimes as you see it can be x = -1 or x = -2.

If the invariant line is vertical, then the object moves or is stretched horizontally. But if the invariant line is horizontal (in some cases it is the x-axis). then the stretch is done vertically. The image will be vertically above the object.

Thanks again Dark Destination. You've helped me a lot. Got it this time!

 

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