Question

quadrilateral abcd is the result of dilating quadrilateral abcd about point p by a scale factor of 3.
determine whether each claim about the properties of abcd and abcd is true or false.
the measures of ∠b and ∠b are equal. true/false
ab and ab are both perpendicular to the x - axis. true/false

Explanation:

For the claim "The measures of $\boldsymbol{\angle B}$ and $\boldsymbol{\angle B'}$ are equal."

Step1: Recall dilation properties

Dilation is a similarity transformation. Similar figures have corresponding angles equal.

Step2: Apply to angles

Since $A'B'C'D'$ is a dilation of $ABCD$ (so they are similar), corresponding angles $\angle B$ and $\angle B'$ are equal.

Step1: Analyze $\overline{AB}$

From the graph, $\overline{AB}$ is vertical (same $x$-coordinate for $A$ and $B$), so it's perpendicular to the $x$-axis (which is horizontal).

Step2: Analyze dilation effect on $\overline{AB}$

Dilation about point $P$ with scale factor 3 preserves the direction of segments. Since $\overline{AB}$ is vertical, its image $\overline{A'B'}$ (after dilation) will also be vertical (same direction), hence perpendicular to the $x$-axis.

Answer:

True

For the claim " $\boldsymbol{\overline{AB}}$ and $\boldsymbol{\overline{A'B'}}$ are both perpendicular to the $\boldsymbol{x}$-axis."