Enlargement Ray Method Demonstration This resource provides animated

Enlargement – Ray Method – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

What can we say about the shadow? Is it congruent? … similar?

If we double the length of the equal sides of an isosceles triangle, what happens to the length of the third side?

If we double the length of the equal sides of an isosceles triangle, what happens to the length of the third side?

If we double the length of the equal sides of an isosceles triangle, what happens to the length of the third side? 5 cm 3 cm 5 cm 10 cm 6 cm These are similar triangles. They are the same shape at different sizes. 10 cm

Sketch these triangles. Choose a scale factor (× 2, × 3, × 0. 5) to extend both sides & enlarge the triangle. What happens to the third length? 3 cm ? 5 cm 4 cm ? 2 cm 5 cm ?

If we want to enlarge a line by a scale factor of 2, we can measure the distance from a point to each end & double it. This is the ray method of enlargement.

If we want to enlarge a line by a scale factor of 2, we can measure the distance from a point to each end & double it.

If we want to enlarge a line by a scale factor of 2, we can measure the distance from a point to each end & double it.

If we want to enlarge a shape by a scale factor of 2, we can measure the distance from a point to each vertex & double it. This is the ray method of enlargement.

The cross-sections of cones & pyramids are all similar shapes. Square-Based Pyramid We can think of the apex as the centre of enlargement. Cone Irregular pentagon

If this was one photograph, which is larger? We must know distance to gauge size.

To know the size of something you must know its distance from you. 2 eyes means 3 D sight & depth perception.

Without a grid, we can use the ray method to enlarge shapes. Enlarge Shape A by a scale factor of 2. 6 cm A We could enlarge from any point. Measure the distance from the centre of enlargement to each vertex. Multiply the distance by 2 & plot the image vertices. Check your accuracy by measuring side lengths. ①

Enlarge Shape B by a scale factor of 3. Choose your own centre of enlargement. B Measure the distance from the centre of enlargement to each vertex. Multiply the distance by 3 & plot the image vertices. Check your accuracy by measuring side lengths. ②

Find the centre of enlargement used to enlarge shape C. C ③

④ Using the ray method, enlarge shape D by a scale factor of 0. 5. D To find the new vertex, we will half the length from the original to the centre of enlargement.

How can we use the ray method to enlarge shape E by a scale factor of − 1? E The new image vertices are the same distance from the centre of enlargement but in the opposite direction.

Is the ray method accurate? What do you think it is still used for? The ray method was used for construction & architecture. It is also used in art & computer games. Parallel lines converge at the ‘vanishing point’: this creates perspective in a 2 D image.

The Ray Method Enlarge each shape by the given Scale Factor using the given centre of enlargement. Check our answers by measuring side lengths. 1 2 SF 3 SF 2 3 SF 1. 5 SF 0. 5 4

The Ray Method Enlarge each shape by the given Scale Factor using the given centre of enlargement. Check our answers by measuring side lengths. 1 2 SF 3 SF 2 3 SF 1. 5 SF 0. 5 4

The Ray Method Enlarge each shape by the given Scale Factor using the given centre of enlargement. Check our answers by measuring side lengths. 1 1 2 2 SF 3 SF 2 3 3 SF 1. 5 SF 0. 5 SF 3 SF 2 SF 1. 5 4 SF 0. 5 4

Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths. co. uk