Question

Question 1-1
Determine the coordinates of A” when CASH is reflected over x=2 followed by (x,y) → (x-1, y-5).

Answer 1

The coordinates of A'' are $A''(x,y) = (3-x, y-5)$.

Let be $A(x,y) = (x,y)$, we apply the following operations to get the coordinates of A'':

Reflection over x = 2

$A'(x,y) = (x,y) + 2\cdot [(2,y)-(x,y)]$

$A'(x,y) = (x,y) +2\cdot (2-x, 0)$

$A'(x,y) = (x,y) +(4-2\cdot x, 0)$

$A'(x,y) = (4-x, y)$

Translation

$A''(x,y) = (4-x, y) +(-1, -5)$

$A''(x,y) = (3-x, y-5)$

The coordinates of A'' are $A''(x,y) = (3-x, y-5)$.

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