The scale on a map is 1 in : 330 mi. The map distance between two cities is 12 in. Find the actual distance between the two citi
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Given the triangle
PQR
with points
P(8,0)
Q(6,2)
R(-2,-4)
And the triangle
P'Q'R'
with points
P'(4,0)
Q'(3,1)
R'(-1,-2)
Part A. Scale factor
Using the vertex
P( 8, 0)
P'(4,0)
the dilatation factor is given by
The triangle has a dilatation factor of 1/2
Part B:
P''Q''R'' after using P'Q'R' reflected about the y axis
to make a reflection over the y axis
coordinates (x,y) turn into coordinates (-x,y)
as follows
Then triangle P''Q''R'' has coordinates
P''(-4,0)
Q''(-3,1)
R''(1,-2)
Part C:
PQR is congruent to P''Q''R''?
Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.
Then the triangles are not congruent
Step-by-step explanation:
We have
First, 125 is a perfect cube because
and
x^3 is a perfect cube because
so we can use the difference of cubes identity
Let say we have two perfect cubes:
64 because 8×8×8=64
and 27 because 3×3×3=27 and let subtract
we know that
but using the difference of cubes identity we should get the same thing.
Remeber cube root of 64 is 4 and cube root of 27 is 3 so we have
So the difference of cubes works for real numbers. This is a good way to help remeber the identity using real numbers.
Back on to the topic,
we know that 5 is cube root of 125 and x is the cube root of x^3 so we have