Triangle ABC is shown on the graph. What are the coordinates of the image of point B after the triangle is rotated 270° about the origin? (4, 2) (2, 4) (–4, –2) (–2, –4)

(4, 2).The Answer is A.Further explanationFor a counterclockwise rotation of 270° about the origin, symbolized by [tex]\boxed{ \ Rot_{270} \ }[/tex], the vertex matrix as a multiplier is [tex]\left[\begin{array}{ccc}0&1\\-1&0\\\end{array}\right].[/tex]State (x, y) as the initial coordinate and (x', y') as the final coordinate.The results of rotation are obtained from the multiplication of the matrix with the initial coordinates.  [tex]\left[\begin{array}{ccc}x'\\y'\\\end{array}\right] = \left[\begin{array}{ccc}0&1\\-1&0\\\end{array}\right]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}x'\\y'\\\end{array}\right] = \left[\begin{array}{ccc}(0)(x) + (1)(y)\\(-1)(x) + (0)(y)\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}x'\\y'\\\end{array}\right] = \left[\begin{array}{ccc}y\\-x\\\end{array}\right][/tex]It can be concluded that if a point is rotated 270° about the origin, the rule that describes the transformation is [tex]\boxed{ \ (x, y) \rightarrow (y, -x) \ }[/tex]Let's consider the key problem.Triangle ABC with coordinates of points A (-5, 3), B (-2, 4), and C (-2, 2) is rotated 270° about the origin. Let's find out the rotation results called A', B', and C' implementing the rule.[tex]\boxed{ \ (x, y) \rightarrow (y, -x) \ }[/tex][tex]\boxed{ \ A(-5, 3) \rightarrow A'(3, 5) \ }[/tex][tex]\boxed{ \ B(-2, 4) \rightarrow B'(4, 2) \ }[/tex][tex]\boxed{ \ C(-2, 2) \rightarrow C'(2, 2) \ }[/tex]Hence,  the coordinates of the image of point B after the triangle is rotated 270° about the origin is B' (4, 2).Learn moreThe similar problem a line K that passes through (3, 5) but not parallel to either x-axis or y-axis   composite function : triangle ABC, is shown on the graph, rotated 270° about the origin, rotation,degrees, transformation geometry, translation, reflection, dilation, multiplier, vertex matrix, initial coordinate, the image, rule, describes