Question

1. graph the image of trapezoid jklm after a dilation with a scale factor of $\frac{1}{5}$, centered at the origin.

Explanation:

Step1: Identify trapezoid vertices

Assume vertices of trapezoid $JKLM$ are $J(x_J,y_J)$, $K(x_K,y_K)$, $L(x_L,y_L)$, $M(x_M,y_M)$. From the graph, if we estimate (assuming integer - valued coordinates for simplicity), say $J(5, - 10)$, $K(5,5)$, $L(10,10)$, $M(10,0)$.

Step2: Apply dilation formula

The formula for dilation centered at the origin with scale factor $k=\frac{1}{5}$ is $(x',y')=(k x,k y)$.
For point $J$: $x_J'=\frac{1}{5}\times5 = 1$, $y_J'=\frac{1}{5}\times(- 10)=-2$.
For point $K$: $x_K'=\frac{1}{5}\times5 = 1$, $y_K'=\frac{1}{5}\times5 = 1$.
For point $L$: $x_L'=\frac{1}{5}\times10 = 2$, $y_L'=\frac{1}{5}\times10 = 2$.
For point $M$: $x_M'=\frac{1}{5}\times10 = 2$, $y_M'=\frac{1}{5}\times0 = 0$.

Step3: Graph new trapezoid

Plot the new points $J'(1,-2)$, $K'(1,1)$, $L'(2,2)$, $M'(2,0)$ on the coordinate - plane and connect them to form the dilated trapezoid.

Answer:

Graph the trapezoid with vertices $(1,-2)$, $(1,1)$, $(2,2)$, $(2,0)$ on the same coordinate - grid as the original trapezoid.