1.
We are told that the coordinates of the image are of the formula:
P'(x-2 , y-3) where x and y are the actual points and x-2 and y-3 are the reflections
Finding the coordinates of point A:
We are given that the coordinates of reflection of A are: A'(-4 , 3)
we also know that reflected point follow the formula: P'(x-2 , y-3)
So, the points of A'(-4 , 3) follow the formula P'(x-2 , y-3)
So, their respective x and y coordinates will be equal
Hence,
x - 2 = -4
x = -2 [adding 2 on both sides]
Also,
y - 3 = 3
y = 6 [adding 3 on both sides]
Therefore, the coordinates of A are A(-2,6)
Finding the coordinates of B:
We are given the coordinates of B' are B'(-4 , 2)
So,
x - 2 = -4
x = -2 [adding 2 on both sides]
also,
y-3 = 2
y = 5 [adding 5 on both sides]
Therefore, the coordinates of B are: B(-2,5)
Finding the coordinates of C:
We are given that the coordinates of reflection of C are: C'(-2,3)
Using the general formula given in the question:
x - 2 = -2
x = 0 [adding 2 on both sides]
y - 3 = 3
y = 6 [adding 3 on both sides]
Therefore, the coordinates of C are: C(0,6)
Finally, the coordinates of A, B and C are:
A(-2,6) , B(-2,5) , C(0,6)
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2.
Reflecting the pre-image along the x-axis
To reflect along x-axis, we multiply the y-coordinate by -1
Coordinates of the pre-image:
A(-2,6) , B(-2,5) , C(0,6)
Coordinates of points reflected along the x-axis:
A(-2,-6) , B(-2,-5) , C(0,-6)