Question

Quadrilateral ABCD with vertices A(0, 6), B(-3, -6), C(-9.-6), and D(-12, -3):

a) dilation with scale factor of 1/3 centered at the origin
b) translation along the vector (-5, -1)

Answer 1

Part (a)

Answers:

A' = (0, 2)

B' = (-1, -2)

C' = (-3, -2)

D' = (-4, -1)

Step-by-step explanation:

Multiply each coordinate by 1/3.

For instance,

`B(-3,-6) \to B( -3*(1/3), -6*(1/3) ) \to B \ '(-1, -2)`

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Part (b)

Answers:

A' = (-5, 5)

B' = (-8, -7)

C' = (-14, -7)

D' = (-17, -4)

Step-by-step explanation:

Subtract 5 from the x coordinate. Subtract 1 from the y coordinate. This moves each point 5 units to the left and 1 unit down.

I'll show an example using point C.

`(\text{x},\text{y})\to(\text{x}-5,\text{y}-1)\\\\(-9,-6)\to(-9-5,-6-1)\\\\(-9,-6)\to(-14,-7)\\\\`

Therefore, C(-9,-6) moves to C ' (-14,-7)