Question 1003846
The vertices of a triangle are A(8,-24), B(8,-8) and C(16,-8).
If the triangle is dilated by a scale factor of 1/4, what will
be the coordinates of A'?
<pre>
Since you did not state the center of dilation, I will
assume you meant the center of dilation to be the origin.

A(8,-24), B(8,-8) and C(16,-8)

{{{drawing(2000/7,400,-2,18,-26,2,grid(.5),

line(-3,0,29,0),line(0,-27,0,3), red(triangle(8,-24,8,-8,16,-8),
line(8,-24,8,-8),line(8,-24,16,-8),line(8,-8,16,-8)),
locate(8.1,-24,A),locate(8.1,-8,B),locate(16.1,-8,C),
triangle(2,-20,2,-26,2,-22),
triangle(4,-20,4,-26,4,-22),
triangle(6,-20,6,-26,6,-22),
triangle(8,-24,8,-26,8,-25),
triangle(10,-20,10,-26,10,-22),
triangle(12,-20,12,-26,12,-22),
triangle(14,-20,14,-26,14,-22),
triangle(16,-20,16,-26,16,-22)

) )}}}

In that case, we multiply all the coordinates of

A(8,-24), B(8,-8) and C(16,-8)

by 1/4, and get 

A'(2,-6), B'(2,-2) and C'(4,-2)

We draw the dilated triangle A'B'C' in red also, and
green lines from the origin through the coordinates:

{{{drawing(2000/7,400,-2,18,-26,2,grid(.5),

green(line(0,0,8,-24),line(0,0,8,-8),line(16,-8,0,0)),


line(-3,0,29,0),line(0,-27,0,3), red(triangle(8,-24,8,-8,16,-8),
line(8,-24,8,-8),line(8,-24,16,-8),line(8,-8,16,-8)),
locate(8.1,-24,A),locate(8.1,-8,B),locate(16.1,-8,C),
triangle(2,-20,2,-26,2,-22),
triangle(4,-20,4,-26,4,-22),
triangle(6,-20,6,-26,6,-22),
triangle(8,-24,8,-26,8,-25),
triangle(10,-20,10,-26,10,-22),
triangle(12,-20,12,-26,12,-22),
triangle(14,-20,14,-26,14,-22),
triangle(16,-20,16,-26,16,-22),

red(triangle(2,-6,2,-2,4,-2),
line(2,-6,2,-2),line(2,-6,4,-2),line(2,-2,4,-2)),
locate(2.1,-6,"A'"),locate(2.1,-2,"B'"),locate(4.1,-2,"C'")

) )}}}

I know you just wanted A' but you need to understand what's
going on, not just a cookbook way to get an answer.  It's
very hard to learn math the cookbook way without understanding
what's going on.  Understanding is what makes math easy.

Edwin</pre>