Answer:
see attached diagram
Step-by-step explanation:
Given triangle has vertices at points B(-5,3), C(-5,7) and D(1,7). The center of dilation is point A(-1,3) and the factor of dilation is [tex]\dfrac{1}{2}.[/tex] The dilation by a factor [tex]\dfrac{1}{2}[/tex] decreases lengths AB, AC and AD twice, then image triangle vertices are midpoints of segments AB, AC and AD.
1. The midpoint E of the segment AB has coordinates
[tex]E\left(\dfrac{-5+(-1)}{2},\dfrac{3+3}{2}\right)\Rightarrow E(-3,3).[/tex]
2. The midpoint F of the segment AC has coordinates
[tex]F\left(\dfrac{-5+(-1)}{2},\dfrac{7+3}{2}\right)\Rightarrow F(-3,5).[/tex]
3. The midpoint G of the segment AD has coordinates
[tex]G\left(\dfrac{1+(-1)}{2},\dfrac{3+7}{2}\right)\Rightarrow G(0,5).[/tex]
