The coordinates of the vertices of △DEF are D(2,3),E(4,0), and F(1,−2). The coordinates of the vertices of △TVW are T(0,3), V(−2,0), and W(1,−2).Which series of transformations correctly shows that △DEF≅△TVW?a reflection over the y-axis and a translation 2 units righta reflection over the x-axis and a translation 2 units downa reflection over the x-axis and a translation 2 units up
Q. The coordinates of the vertices of △DEF are D(2,3),E(4,0), and F(1,−2). The coordinates of the vertices of △TVW are T(0,3), V(−2,0), and W(1,−2).Which series of transformations correctly shows that △DEF≅△TVW?a reflection over the y-axis and a translation 2 units righta reflection over the x-axis and a translation 2 units downa reflection over the x-axis and a translation 2 units up
Reflect over y-axis: Step 1: Reflect /_DEF over the y-axis.To reflect a point (x,y) over the y-axis, change the x-coordinate to −x. So:D(2,3) becomes D'(−2,3),E(4,0) becomes E'(−4,0),F(1,−2) becomes F'(−1,−2).
Translate 2 units right: Step 2: Translate D′, E′, F′2 units to the right.To translate a point (x,y)2 units right, add 2 to the x-coordinate. So:D′(−2,3) becomes D′′(0,3),E′0 becomes E′1,E′2 becomes E′3.
Compare coordinates after transformations: Step 3: Compare the coordinates of △TVW with △DEF after transformations.T(0,3), V(−2,0), and W(1,−2) are the coordinates of △TVW.D′′(0,3), E′′(−2,0), and F′′(1,−2) are the coordinates of △DEF after transformations.The coordinates match, indicating that △DEF is congruent to △TVW after the specified transformations.
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