Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(8, 0), Q(6, 2), and R(−2, −4). Triangle P'Q'R' has vertices P'(4, 0), Q'(3, 1), and R'(−1, −2). Plot triangles PQR and P'Q'R' on your own coordinate grid. Part A: What is the scale factor of the dilation that transforms triangle PQR to triangle P'Q'R'? Explain your answer. (4 points) Part B: Write the coordinates of triangle P"Q"R" obtained after P'Q'R' is reflected about the y-axis. (4 points) Part C: Are the two triangles PQR and P''Q''R'' congruent? Explain your answer. (2 points)

Part A: The scale factor is 2

Part B:

P''(-4, 0)

Q''(-3, 1)

R''(1, -2)

Part C: No

Step-by-step explanation:

Part A:

The coordinates of the triangle PQR are P(8, 0), Q(6, 2), and R(-2, -4)

The coordinates of the triangle P'Q'R' are P'(4, 0), Q'(3, 1), and R'(-1, -2)

Please find attached the plot of triangles PQR and P'Q'R'

The length of the sides are given by the following formula;

Using an online length

For PQ. the length =

For PR. the length =

For RQ. the length =

While for triangle P'Q'R', we have;

For P'Q'. the length =

For P'R'. the length =

For R'Q'. the length =

∴ PQ = 2 × P'Q'

PR = 2 × P'R'

QR = 2 × Q'R'

Therefore, the scale factor = 2

Part B

By reflecting about the y-axis we have;

Coordinates of the preimage (x, y) after reflection across the y=axis becomes (-x, y)

Therefore, the coordinates of the triangle P''Q''R'' are;

P'(4, 0) after reflection = P''(-4, 0)

Q'(3, 1) after reflection about the y-axis is Q''(-3, 1)

R'(-1, -2) after reflection about the y-axis becomes R''(1, -2)

Part C: No

Given that the triangle P''Q''R'' is congruent to triangle P'Q'R', and triangle P'Q'R' is similar to but not congruent to triangle PQR, we have that triangle P''Q''R'' is similar to but not congruent to triangle PQR.

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights