Triangle ABC has vertices&nbsp;A(1,3),B(−2,−1)&nbsp;and&nbsp;C(3,−2). Graph&nbsp;△ABC&nbsp;and its image after the indicated composite transformation.First transformation: Translation: along&nbsp;(x,y)→(x+2,y)Second Transformation: Reflection across y-axis.Coordinate of B after translationB'( ?, ?).Coordinate of B after ReflectionB''( ?, ?)

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Triangle ABC has vertices&amp;nbsp;A(1,3),B(−2,−1)&amp;nbsp;and&amp;nbsp;C(3,−2). Graph&amp;nbsp;△ABC&amp;nbsp;and its image after the indicated composite transformation.First transformation: Translation: along&amp;nbsp;(x,y)→(x+2,y)Second Transformation: Reflection across y-axis.Coordinate of B after translationB&#039;( ?, ?).Coordinate of B after ReflectionB&#039;&#039;( ?, ?)

Nathalie Frazier · Accepted Answer

Given the vertices of triangle ABC are&amp;nbsp;A(1,3),B(−2,−1)&amp;nbsp;and&amp;nbsp;C(3,−2).Let graph this triangle.First transformation: translation: along&amp;nbsp;(x,y)→(x+2,y).After this translation, The triangle&#039;s three vertices should be written.A(1,3)=A′(1+2,3)=A′(3,3).B(−2,−1)=B′(−2+2,−1)=B′(0,−1).C(3,−2)=C′(3+2,−2)=C′(5,−2).After first transformation the triangle A&#039;B&#039;C&#039; would look like,Second transformation: Reflection across y axis.When we reflect a point across the y axis, the y coordinate remains the same, but the x coordinate is transformed into it&#039;s opposite (it&#039;s sign is changed).The reflection of the point (x, y) across the y axis is point (-x, y).A′(3,3)=A&amp;nbsp;″(−3,3)B′(0,−1)=B&amp;nbsp;″(0,−1)C′(5,−2)=C&amp;nbsp;″(−5,−2)Let&#039;s sketch a triangle. A&#039;&#039;B&#039;&#039;C&#039;&#039;.

Triangle ABC has vertices A(1, 3), B(-2, -1)\ \text{and}\ C(3,

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