Question

Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below: Two rectangular tiles, rectangle PQRS with vertices at P 5, 7. Q is at 9, 7. R is at 9, 12. S is at 5, 12 . Rectangle JKLM with vertices J at 4, 5; K at 6, 5; L at 6, 10; and M at 4, 10. Which statement is correct?

Answer 1

Full question :

Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below: Two rectangular tiles, rectangle PQRS with vertices at P 5, 7. Q is at 9, 7. R is at 9, 12. S is at 5, 12 . Rectangle JKLM with vertices J 4, 5. K is at 6, 5. L is at 6, 10. M is at 4, 10. Which statement is correct? The two tiles are not similar because segment PQ is to segment QR is 4:5 and segment JK is to segment LM is 2:1. The two tiles are not similar because segment SP is to segment SR is 5:4 and segment MJ is to segment ML is 5:2. The two tiles are similar because segment PQ is to segment QR is 4:5 and segment JK is to segment KL is also 4:5. The two tiles are similar because segment SR is to segment ML is 2:1 and segment PQ is to segment JK is also 2:1.

Answer:

The two tiles are not similar because segment SP is to segment SR is 5:4 and segment MJ is to segment ML is 5:2.

Step-by-step explanation:

Given vertices which will be our points on the graph to trace the rectangular shapes:

For the first rectangular shape PQRS

P(5,7)

Q(9,7)

R(9,12)

S(5,12)

For the second rectangular shape JKLM

J(4,5)

K(6,5)

L(6,10)

M(4,10)

From the above we can find that the two tiles are not similar if we calculate using their x, y coordinates points(vertices) on the graph.

We can see from the options given that only the second option is correct because:

Line SP ratio to line SR in rectangle PQRS= 5:4

since SP=12-7=5 and SR=9-5=4

Therefore SP:SR = 5:4

Line MJ ratio to line ML in rectangle JKLM= 5:2

Since MJ= 10-5=5 and ML= 6-4=2

Therefore MJ:ML =5:2