Question

what a hot streak, a 4 win streak
4
quadrilateral abcd is the result of dilating quadrilateral abcd about point a by a scale factor of \\(\frac{1}{2}\\).
graph of quadrilateral abcd on a coordinate plane with a at (4,0), b at (-1,-4), c at (1,0), d at (4,3)
determine whether each claim about the properties of abcd and abcd is true or false.
the lengths of \\(\overline{ab}\\) and \\(\overline{ab}\\) are equal, true/false
\\(\overline{ab}\\) and \\(\overline{ab}\\) are on distinct parallel lines. true/false

Explanation:

First Claim: The lengths of $\boldsymbol{\overline{AB}}$ and $\boldsymbol{\overline{A'B'}}$ are equal.

Step1: Recall Dilation Property

Dilation scales lengths by the scale factor. The scale factor here is $\frac{1}{2}$, so $A'B' = \frac{1}{2}AB$.

Step2: Compare Lengths

Since $\frac{1}{2}AB
eq AB$ (unless $AB = 0$, which it's not), their lengths aren't equal.

Step1: Recall Dilation and Parallelism

Dilation preserves the direction of segments. So $\overline{AB}$ and $\overline{A'B'}$ are parallel (same slope) and distinct (different lengths, so different positions).

Step2: Confirm Parallelism

Since dilation about $A$ scales $\overline{AB}$ to $\overline{A'B'}$, they lie on lines with the same slope (parallel) and are distinct (not coinciding).

Answer:

False

Second Claim: $\boldsymbol{\overline{AB}}$ and $\boldsymbol{\overline{A'B'}}$ are on distinct parallel lines.