L42.54 is the same as 42 _____' 24". Answer:

1 answer:

3 0

There are 60 ( ' ) minutes in 1 degree, and 60 ( " ) seconds in 1 minute.

now, on a Latitude of 42.54°, there are 42° clearly, how much is the 0.54 anyway?

well, we know there are 60 minutes in 1 degree, therefore 0.54 * 60 is how many minutes in 0.54, or 32.4'. So a whole 32' and 0.4 of a minute.

how many seconds in 0.4 minutes? well, there are 60 seconds in 1 minute, thus 0.4* 60, or 24.

L42.54 is then 42° 32' 24".

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The scale factor of the dillation that transforms triangle PQR to triangle P'Q'R' is $\frac{1}{3}$ .

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There is a typographical mistake in the statement. Correct statement is:

<em>Triangle PQR is transformed to triangle P'Q'R. Triangle PQR has vertices P (3, -6), Q (0, -9), and R (-3,0). Triangle P'Q'R has vertices P' (1, -2), Q' (0,-3), and R' (-1, 0). What is the scale factor of the dilation that transforms triangle PQR to triangle P'Q'R? Explain your answer.</em>

From Linear Algebra we define dillation with respect to a given point as:

$(x',y') = O(x,y)+k\cdot (x,y)$ (Eq. 1)

Where:

$O(x,y)$ - Origin, dimensionless.

$k$ - Scale factor, dimensionless.

$(x,y)$ - Original point, dimensionless.

$(x',y')$ - Dilated point, dimensionless.

If we consider that $O(x,y) = (0,0)$ and we know that $P(x,y) =(3,-6)$ , $Q(x,y) =(0,-9)$ , $R(x,y) =(-3,0)$ , $P'(x,y) =(1,-2)$ , $Q'(x,y) =(0,-3)$ and $R'(x,y) = (-1,0)$ , then scale factor of each point is, respectively: