△pqr is reflected to form △p′q′r′ . the vertices of △pqr are p(1,1) , q(−1,−2) , and r(4,−2) . the vertices of △p′q′r′ are p′(−1,1) , q′(1,−2) , and r′(−4,−2) . which reflection results in the transformation of △pqr to △p′q′r′ ? reflection across the x-axis reflection across the y-axis reflection across y = x reflection across y=−x

The △PQR is reflected across the y-axis and option 2 is correct.

Step-by-step explanation:

1. The reflection across the x-axis is defined as

2. The reflection across the y-axis is defined as

3. The reflection across the y=x is defined as

4. The reflection across the y=-x  is defined as

It is given that the vertices of △PQR are P(1,1) , Q(−1,−2) , and R(4,−2) . The vertices of △P′Q′R′ are P′(−1,1) , Q′(1,−2) , and R′(−4,−2) .

The relation between prerimage and image is defined as

Therefore the △PQR is reflected across the y-axis and option 2 is correct.

step-by-step explanation:

one of the most important purposes of surface treatment is to alter surface properties according to the requirement of specific applications. for example, hydrophobic coating has been utilized on windshield and eyeglasses. gold atom monolayer on substrate has become a popular surface bioconjugation strategy.  

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet