Answer :

iGreen
Question #1:

a)

(4, 2)

Both of these are positive, and when x and y are both positive they're both in Quadrant 1.

b)

(x + 1, y - 5)

Add 1 to 'x', subtract 5 from 'y':

(4 + 1, 2 - 5)

(5, -3)

x is positive and y is negative, that means this will be in Quadrant 4.

c)

Reflection Across y-axis:

(-x, y)

Multiply -1 to 'x':

(5 * -1, -3)

(-5, -3)

Both of these are negative, if both x and y are negative it's located in Quadrant 3.

Question #2:

No, that can't tessellate a plane. We can't cover up space so there are no overlaps or gaps.
Hippalectryon
a) A(4,2) : 4>0, 2>0 hence it's in the first quadrant
b) A'(4+1,2-5)=A'(5,-3); 5>0, -3<0 hence it's in the fourth quadrant
c) A''(-5,-3) : -5<0, -3<0 hence it's in the third quadrant.

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You cannot tessellate the plane with such a figure.
Here's why :

Let's try to add a second figure to fill the empty space.
* we cannot add it that way [see the first picture attached] because we won't be able to fill the inside of the circle created
* we cannot fill it that way either [see the second picture attached]. Indeed, that would imply that we'd need to cover the space using that next figure [see the third picture attached], which ones again creates an un-fillable circle.
View image Hippalectryon
View image Hippalectryon
View image Hippalectryon

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