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(1, 1), Q(7, 1), R(7, 5), and S(1, 5). Rectangle JKLM with vertices J(2, 1) , K(11, 1), L(11, 7) and M(2, 7) Which statement is correct? The two tiles are similar because segment SR is to segment SP is 3 : 2 and segment ML is to segment MJ is also 3 : 2. The two tiles are not similar because segment PQ is to segment QR is 6 : 4 and segment JK is to segment KL is 9 : 8. The two tiles are not similar because segment SP is to segment SR is 4 : 7 and segment MJ is to segment ML is 2 : 3. The two tiles are similar because segment PQ is to segment QR is 6 : 5 and segment JK is to segment KL is also 6 : 5.

Answer 1

From our diagram we can infer that the measure of segment SR is 6, the measure of segment SP is 4, the measure of segment ML is 9, and the measure of segment MJ is 6.
$\frac{SR}{SP} = \frac{6}{4} = \frac{3}{2}$ segment SR is to segment SP  3 : 2

$\frac{ML}{MJ} = \frac{9}{6} = \frac{3}{2}$ segment ML is to segment MJ also 3 : 2

We can conclude that the correct statement is: "The two tiles are similar because segment SR is to segment SP is 3 : 2 and segment ML is to segment MJ is also 3 : 2"