Question

Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below.
Which statement is correct?
A.) The two tiles are similar because is 1 : 3 and is also 1 : 3.
B.) The two tiles are similar because is 3 : 2 and is also 3 : 2.
C.) The two tiles are not similar because is 1 : 6 and is 1 : 3.
D.) The two tiles are not similar because is 5 : 1 and is 2 : 3.

Answer 1

use the distance formula to find the length and breadth of the tiles

Answer 2

breadth?

Answer 3

Take point S and point P from the largest rectangle. What is the size of this side? It's the the y coordinate from the point above (S) minus the y coordinate from the point below (P). Think about it this way: the y-axis gives us the height, so, when we take the change in y, we get the height. Can you tell me what did you get for this side and for the height of the smaller rectangle?

Answer 4

so i do (Y2-Y1) + (X2-X1)

Answer 5

The distance formula should be: \( \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2} \) but notice that, because the side is parallel to the y axis, the change in x = 0. In other words, x2 - x1 = 0 :-)

Answer 6

The opposite happens for the side SR: It's parallel to the x axis, y2-y1 = 0. So the formula becomes quite simple :-)

Answer 7

lol im, confused now

Answer 8

Look S and R: what are their x coordinates? Remember, (x-coordinate, y-coordinate)

Answer 9

(8-8) and (4-2)

Answer 10

No, no. S has coordinates (2,8) and P is (2,2). So, what are their x coordinates?

Answer 11

the x is 2

Answer 12

Correct. So, what is x(from S) - x (from P)? :-)

Answer 13

0

Answer 14

So, what's the height? What is the distance using the formula above?

Answer 15

(0,6)?

Answer 16

That's partially correct. When we calculate distance, we are looking for a number, not a point. It is 6.

Answer 17

oh ok

Answer 18

So, do the same for the smaller rectangle, points M and J. The formula is the same. What did you get?

Answer 19

its 3

Answer 20

??????

Answer 21

Correct :-)

Answer 22

Now, the ratio of heights is 6:3. Now, we have to discover the ratio of the other side, that is, breadth. What is the distance between Q and P?

Answer 23

The formula is the same, but now note that y(from point Q) - y (from point P) = 0.

Answer 24

it will be 6 :3

Answer 25

right?

Answer 26

For the height, yeah. We need to find the breadth one now.

Answer 27

is it 1:1?

Answer 28

No. 1 is the distance for the smaller rectangle, but the largest one is not 1.

Answer 29

oh i assumed that because i looked at letter C

Answer 30

Haha. No. The ratio we need to find (to answer the question) is the ratio of breadth/height of the rectangle, not height/height between them. You need to find the distance between Q and P :-)

Answer 31

oh ok lol, so how do i find the breadth?

Answer 32

It's the distance between Q and P for the larger rectangle and between K and J for the smaller one.

Answer 33

ok so x = 2 right?

Answer 34

Yup. Now, the ratio will be breadth/height for the two rectangles. Breadth = 2, Height = 6 in the first rectangle, and Breadth = 1 and height = 3 in the second rectangle. What is the ratio, then?

Answer 35

2:6 and 1:3?

Answer 36

Yes. But 2:6 is what? Simplify it.

Answer 37

1:3

Answer 38

Correct. So, what is the answer?

Answer 39

A :)

Answer 40

Correct. Well done :-)

Answer 41

thanks for your help, i appreciate it :)