Question

dilating a segment in the coordinate plane
the rule ( d_{o,0.25}(x,y)\to(0.25x,0.25y) ) is applied to the segment lm to make an image of segment ( lm ), not shown.
the coordinates of ( l ) in the image are ( (-1,2) ).
the coordinates of ( m ) in the image are ( (1,2) ).
the length, ( lm ), is 2.
the slope of the original segment and dilated segment are both zero.
x both 0.25
both undefined
not the same
both zero

Explanation:

Step1: Find coordinates of \(L\) and \(M\)

From the graph, \(L(- 4,8)\) and \(M(4,8)\).

Step2: Apply the dilation rule \(D_{O,0.25}(x,y)=(0.25x,0.25y)\)

For \(L(-4,8)\), \(L'=(0.25\times(-4),0.25\times8)=(-1,2)\)
For \(M(4,8)\), \(M'=(0.25\times4,0.25\times8)=(1,2)\)

Step3: Calculate the slope of \(LM\)

Slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). For \(L(-4,8)\) and \(M(4,8)\), \(m_{LM}=\frac{8 - 8}{4-(-4)}=\frac{0}{8}=0\)

Step4: Calculate the slope of \(L'M'\)

For \(L'(-1,2)\) and \(M'(1,2)\), \(m_{L'M'}=\frac{2 - 2}{1-(-1)}=\frac{0}{2}=0\)

So the slope of the original segment \(LM\) and dilated segment \(L'M'\) are both zero.

Answer:

The slope of the original segment and dilated segment are both zero.