Question

1. dilate triangle lmn

center of dilation: (0, 0) scale factor: (\frac{3}{2})

Explanation:

Step1: Identify original coordinates

First, find the coordinates of points \( L \), \( M \), and \( N \) from the graph.

• \( L \) is at \( (-6, 0) \) (since it's 6 units left on the x - axis, y - coordinate 0).
• \( M \) is at \( (0, - 4) \) (on the y - axis, 4 units down).
• \( N \) is at \( (-4, - 2) \) (4 units left on x - axis, 2 units down on y - axis).

Step2: Apply dilation formula

The formula for dilation with center \( (0,0) \) and scale factor \( k=\frac{3}{2} \) is \( (x,y)\to(kx,ky) \).

For point \( L(-6,0) \):

Multiply each coordinate by \( \frac{3}{2} \).
\( x\) - coordinate: \( -6\times\frac{3}{2}=-9 \)
\( y\) - coordinate: \( 0\times\frac{3}{2} = 0 \)
So, \( L'=(-9,0) \)

For point \( M(0, - 4) \):

Multiply each coordinate by \( \frac{3}{2} \).
\( x\) - coordinate: \( 0\times\frac{3}{2}=0 \)
\( y\) - coordinate: \( - 4\times\frac{3}{2}=-6 \)
So, \( M'=(0, - 6) \)

For point \( N(-4, - 2) \):

Multiply each coordinate by \( \frac{3}{2} \).
\( x\) - coordinate: \( -4\times\frac{3}{2}=-6 \)
\( y\) - coordinate: \( - 2\times\frac{3}{2}=-3 \)
So, \( N'=(-6, - 3) \)

Answer:

\( L'(-9,0) \), \( M'(0, - 6) \), \( N'(-6, - 3) \)