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The vertices of ΔABC are A(−3,4)​, B(−2,4)​, and C(−5,2). If ΔABC is reflected across the line y=−2 to produce the image Δ​A'B'C', find the coordinates of the vertex B​'.

The coordinates of B​' after a reflection across the line y= -2

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xero099

The coordinates of vertex B' is [tex]P'(x,y) = (-2, -8)[/tex].

How to calculate the coordinate of point by reflection

A point if reflected across the line [tex]y = -2[/tex] by means of the following formula:

[tex]P'(x,y) = P(x,y)+2\cdot [(x_{P}, -2)-P(x,y)][/tex] (1)

Where:

  • [tex]P(x,y)[/tex] - Original point
  • [tex]x_{P}[/tex] - x-Coordinate of point P
  • [tex]P'(x,y)[/tex] - Resulting point

If we know that [tex]P(x,y) = (-2,4)[/tex] and [tex]x_{P} = -2[/tex], then the coordinates of the vertex is:

[tex]P'(x,y) = (-2, 4) + 2\cdot [(-2,-2)-(-2,4)][/tex]

[tex]P'(x,y) = (-2, 4) +2\cdot (0, -6)[/tex]

[tex]P'(x,y) = (-2, 4) + (0,-12)[/tex]

[tex]P'(x,y) = (-2, -8)[/tex]

The coordinates of vertex B' is [tex]P'(x,y) = (-2, -8)[/tex]. [tex]\blacksquare[/tex]

To learn more on reflections, we kindly invite to check this verified question: https://brainly.com/question/1878272

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