Question

How do I graph the points

Answer 1

Point S is at (-3,6)

The rule $(x,y) \to (x+7,y-9)$ 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)

$x = 0 \to x+7 = 0+7 = 7\\y = 7 \to y-9 = 7-9 = -2$

Which moves to T ' (7,-2)

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Repeat for point U(1,4)

$x = 1 \to x+7 = 1+7 = 8\\y = 4 \to y-9 = 4-9 = -5$

point U ' is located at (8, -5)

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Repeat for V(-5,2)

$x = -5 \to x+7 = -5+7 = 2\\y = 2 \to y-9 = 2-9 = -7$

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.