Point S is at (-3,6)
The rule [tex](x,y) \to (x+7,y-9)[/tex] says to add 7 to the x coordinate and subtract 9 from the y coordinate. This is the same as saying "shift the point 7 units to the right and 9 units down"
Add 7 to the x coordinate: x+7 = -3+7 = 4
Subtract 9 from the y coordinate: y-9 = 6-9 = -3
Point S is at (-3,6) and it moves to S ' (4, -3)
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Do the same to point T(0,7)
[tex]x = 0 \to x+7 = 0+7 = 7\\y = 7 \to y-9 = 7-9 = -2[/tex]
Which moves to T ' (7,-2)
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Repeat for point U(1,4)
[tex]x = 1 \to x+7 = 1+7 = 8\\y = 4 \to y-9 = 4-9 = -5[/tex]
point U ' is located at (8, -5)
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Repeat for V(-5,2)
[tex]x = -5 \to x+7 = -5+7 = 2\\y = 2 \to y-9 = 2-9 = -7[/tex]
Point V moves to V ' (2, -7)
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In summary, the four new translated points are
S ' (4, -3)
T ' (7,-2)
U ' (8, -5)
V ' (2, -7)
The diagram is shown below.
The original trapezoid STUV is shown in blue. The translated trapezoid S'T'U'V' is shown in red.
