Question

1. dilation of 0.5 about the origin

Explanation:

Step1: Recall dilation formula

If a point $(x,y)$ is dilated about the origin by a scale - factor $k$, the new point $(x',y')$ is given by $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Assume coordinates of vertices

Let's assume the coordinates of the vertices of the quadrilateral $PQRS$ are $P(x_1,y_1)$, $Q(x_2,y_2)$, $R(x_3,y_3)$, $S(x_4,y_4)$. For example, if $P(2, - 1)$, $Q(4,0)$, $R(2,2)$, $S(0,0)$.

Step3: Apply dilation

For point $P$ with $k = 0.5$, the new coordinates $P'(x_1',y_1')=(0.5x_1,0.5y_1)$. If $x_1 = 2$ and $y_1=-1$, then $P'(1,-0.5)$. Similarly, for $Q(4,0)$, $Q'(0.5\times4,0.5\times0)=Q'(2,0)$; for $R(2,2)$, $R'(0.5\times2,0.5\times2)=R'(1,1)$; for $S(0,0)$, $S'(0.5\times0,0.5\times0)=S'(0,0)$.

Answer:

The new coordinates of the vertices of the dilated quadrilateral are obtained by multiplying the original coordinates of each vertex by 0.5. The specific new - coordinates depend on the original coordinates of the vertices of the quadrilateral $PQRS$. For example, if the original vertices are as assumed above, the new vertices are $P'(1,-0.5)$, $Q'(2,0)$, $R'(1,1)$, $S'(0,0)$.