Question

dilate figure pqrs by a scale factor of 1/2 with the center of dilation at point p. to dilate the figure, think about the lengths of the corresponding sides. what is the length of pq, the image of segment pq? pq = units

Explanation:

Step1: Recall dilation formula

The length of a dilated segment $A'B'$ with a scale - factor $k$ and the original segment $AB$ and center of dilation at a point is given by $A'B'=k\times AB$. Here, the center of dilation is at $P$, the scale - factor $k = \frac{1}{2}$, and we want to find the length of $PQ'$ (the dilated image of $PQ$).

Step2: Measure original length of $PQ$

By counting the grid units, we find that the length of segment $PQ$ is 6 units.

Step3: Calculate length of $PQ'$

Using the dilation formula $PQ'=k\times PQ$. Substitute $k = \frac{1}{2}$ and $PQ = 6$ into the formula: $PQ'=\frac{1}{2}\times6$.
$PQ' = 3$ units.

Answer:

3