Answer: (x + [-1], y + [1])
Step-by-step explanation:
<em>See attached. </em>We can draw, or picture it in our heads, what the reflection would look like. Then we can pick one (or multiple to test) points and see the translation.
We can also test with a set of points. B', (2, 4) becomes G in the transformation. G is at (1, 5)
(1 - 2, 5 - 4) -> (-1, 1)
Not necessarily.
and
may be linearly dependent, so that their span forms a subspace of
that does not contain every vector in
.
For example, we could have
and
. Any vector
of the form
, where
, is impossible to obtain as a linear combination of these
and
, since
unless
and
.
11/15 + 7 ⇒ rational ⇒ the sum of two rationals is always rational
√14+13 ⇒ irrational ⇒ the sum of a rational and an irrational is always irrational
30×√6 ⇒ irrational ⇒ the product of a nonzero rational and an irrational is always irrational
11/12 × 7/15 ⇒ rational ⇒ the product of two rationals is always rational
