Changing Shapes

1.)Suppose you are going to be designing a logo for a club at your school. To prepare for this product, draw a non-rectangular shape in the coordinate plane so that portions of the shape are in each of the four quadrants. Explain what would happen to your shape if you transformed it using each of the given rules with the center of dilation at the origin.

a. (4x, 4y) b. (0.25x, 0.25y) c. (2x, y)
d. (3x, 3y+5) e. (x+5, y-5) f. (1/2x, 1/2y)

2.) Will any of the transformed figures be similar to the original? Explain.

I have no idea in either two of the questions so help would be appreciated.

Sure, I can help you with these questions!

1) Let's break down each rule and understand what they mean:

a) Rule (4x, 4y): This rule means that each coordinate of the shape is multiplied by 4. So if a point on your shape has coordinates (x, y), after applying this rule, its new coordinates will be (4x, 4y). For example, if your shape has a point at (2, 3), it will transform to (8, 12) after applying this rule.

b) Rule (0.25x, 0.25y): This rule means that each coordinate of the shape is multiplied by 0.25, which is the same as dividing by 4. So if a point on your shape has coordinates (x, y), after applying this rule, its new coordinates will be (0.25x, 0.25y). For example, if your shape has a point at (8, 6), it will transform to (2, 1.5) after applying this rule.

c) Rule (2x, y): This rule means that only the x-coordinate of the shape is multiplied by 2, while the y-coordinate remains the same. So if a point on your shape has coordinates (x, y), after applying this rule, its new coordinates will be (2x, y). For example, if your shape has a point at (3, 5), it will transform to (6, 5) after applying this rule.

d) Rule (3x, 3y+5): This rule means that the x-coordinate is multiplied by 3, while the y-coordinate is multiplied by 3 and then 5 is added to it. So if a point on your shape has coordinates (x, y), after applying this rule, its new coordinates will be (3x, 3y+5). For example, if your shape has a point at (2, 4), it will transform to (6, 17) after applying this rule.

e) Rule (x+5, y-5): This rule means that 5 is added to the x-coordinate, while 5 is subtracted from the y-coordinate. So if a point on your shape has coordinates (x, y), after applying this rule, its new coordinates will be (x+5, y-5). For example, if your shape has a point at (3, 8), it will transform to (8, 3) after applying this rule.

f) Rule (1/2x, 1/2y): This rule means that each coordinate of the shape is multiplied by 1/2, which is the same as dividing by 2. So if a point on your shape has coordinates (x, y), after applying this rule, its new coordinates will be (1/2x, 1/2y). For example, if your shape has a point at (6, 10), it will transform to (3, 5) after applying this rule.

2) Similarity of figures is determined by whether they have the same shape but possibly different sizes. If all the transformed figures have the same shape as the original figure (i.e., the relative positions of the points remain the same), then they are similar.

Considering the given rules, we can see that none of the rules change the shape of the figure without changing its size. This is because each rule preserves the ratios between the coordinates. For example, if two sides of a triangle had a ratio of 1:2 in the original figure, they will still have the same ratio in the transformed figures.

In conclusion, all the transformed figures will be similar to the original figure since they have the same shape but may have different sizes due to the changes in dimensions.

LOL, draw an equilateral triangle with centroid at origin or a circle with center at origin and radius = 1.

for the circle

a it just gets to be a bigger circle (so it is similar)

b same deal, smaller circle but similar.

c try it, I think it will be kind of elliptical (do you know how to prove that?)

d like a but it moves up.

e right and down?

f do you mean 1/(2x) as you wrote it or (1/2)x ? If 1/(2x) then try some points on the circle and see what you get.