General Idea:
When a point or figure on a coordinate plane is moved by sliding it to the right or left or up or down, the movement is called a translation.
Say a point P(x, y) moves up or down ' k ' units, then we can represent that transformation by adding or subtracting respectively 'k' unit to the y-coordinate of the point P.
In the same way if P(x, y) moves right or left ' h ' units, then we can represent that transformation by adding or subtracting respectively 'h' units to the x-coordinate.
P(x, y) becomes 
. We need to use ' + ' sign for 'up' or 'right' translation and use ' - ' sign for ' down' or 'left' translation.
Applying the concept:
The point A of Pre-image is (0, 0). And the point A' of image after translation is (5, 2). We can notice that all the points from the pre-image moves 'UP' 2 units and 'RIGHT' 5 units.
Conclusion:
The transformation that maps ABCD onto its image is translation given by (x + 5, y + 2),
In other words, we can say ABCD is translated 5 units RIGHT and 2 units UP to get to A'B'C'D'.
Setting
, you have
. Then the integral becomes
Now,
in general. But since we want our substitution
to be invertible, we are tacitly assuming that we're working over a restricted domain. In particular, this means
, which implies that
, or equivalently that
. Over this domain,
, so
.
Long story short, this allows us to go from
to
Computing the remaining integral isn't difficult. Expand the numerator with the Pythagorean identity to get
Then integrate term-by-term to get
Now undo the substitution to get the antiderivative back in terms of
.
and using basic trigonometric properties (e.g. Pythagorean theorem) this reduces to
Answer:
isosceles: 2 angles are the same and 2 sides are the same. Equilateral have all the same sides and angles. Saclene have all dfferent angles and sides.
11) isosceles
12) equilateral
13) isosceles or scalene unclear
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Take -920/360 = -2.55555
Take the fraction part -0.5555555 * 360 = -200
The positive of that would be 160 degrees
