XYZ has coordinates X(2, 3), Y(1,4), and Z(8,9). A translation maps X to X'(4,7). What are the coordinates for Y' and Z' for this translation?​

The coordinates are and .

Step-by-step explanation:

First, we have to derive an expression for translation under the assumption that each point of XYZ experiments the same translation. Vectorially speaking, translation from X to X' is defined by:

(1)

Where is the vector translation.

If we know that and , then the vector translation is:

Then, we determine the coordinates for Y' and Z':

The coordinates are and .

radius = 7π

Step-by-step explanation:

The area (A) of a circle = πr² ← r is the radius

The area is given as 49π³ , equating gives

πr² = 49π³ ← divide both sides by π

r² = 49π² ← take the square root of both sides )

r = = 7π