Answer: Choice B
[tex](x,y) \to \left(\frac{5}{2}x,\frac{5}{2}y\right)[/tex]
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Explanation:
When dilating with respect to the origin, any point of the form (x,y) moves to (kx, ky) for some real number k. The k is the scale factor.
Point C is at (-2,2). It moves to C ' (-5,5)
The jump from x = -2 to x = -5 is "times 5/2" since kx = (5/2)*(-2) = -5
The same scale factor is used when going from y = 2 to y = 5.
Both x and y coordinates are multiplied by 5/2 to move from (-2,2) to (-5,5)
Therefore, the dilation rule we use is [tex](x,y) \to \left(\frac{5}{2}x,\frac{5}{2}y\right)[/tex]
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We could have these steps to confirm
[tex](x,y) \to \left(\frac{5}{2}x,\frac{5}{2}y\right)\\\\(-2,2) \to \left(\frac{5}{2}*(-2),\frac{5}{2}(2)\right)\\\\(-2,2) \to (-5,5)\\\\[/tex]
