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Sagot :
Given:
The vertices of a triangle are A (-2, 4) , B (-2,3) , and C (-5,2).
Triangle ABC is reflected across the line y = -1 to produce the image of A'B'C'.
To find:
The coordinate of B' after a reflection across the line y=-1.
Solution:
If a figure is reflected across the line y=b, then
[tex](x,y)\to (x,-(y-b)+b)[/tex]
[tex](x,y)\to (x,-y+b+b)[/tex]
[tex](x,y)\to (x,2b-y)[/tex]
The given triangle ABC is reflected across the line y=-1. So, the rule of reflection is
[tex](x,y)\to (x,2(-1)-y)[/tex]
[tex](x,y)\to (x,-2-y)[/tex]
The coordinates of point B are (-2,3). So,
[tex]B(-2,3)\to B'(-2,-2-3)[/tex]
[tex]B(-2,3)\to B'(-2,-5)[/tex]
Therefore, the coordinates of point B' are (-2,-5).
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