If the green triangle is translated to get the blue triangle in the following image, what is the rule applied for x coordinate and y coordinate respectively?

2 x, \frac{y}{2}

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3 x, \frac{y}{2}

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3 x, \frac{y}{4}

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2 x, \frac{y}{4}

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Solution

The correct option is A $2 x, \frac{y}{2}$

The coordinates of green triangle are (2,0), (1,-2), and (4,-2) respectively.

The coordinates of blue triangle are (4,0), (2,-1), and (8,-1) respectively.

Observing the coordinates, we can determine the following:

Coordinates of green triangle Coordinates of blue triangle Rule

(2,0) (4,0) $(2 x, \frac{y}{2})$

(1,-2) (2,-1) $(2 x, \frac{y}{2})$

(4,-2) (8,-1) $(2 x, \frac{y}{2})$

So, the translation rule applied here is
$x, y \to 2 x, \frac{y}{2}$

∴ Option (a) is correct.

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Coordinates of green triangle	Coordinates of blue triangle	Rule
(2,0)	(4,0)	$(2 x, \frac{y}{2})$
(1,-2)	(2,-1)	$(2 x, \frac{y}{2})$
(4,-2)	(8,-1)	$(2 x, \frac{y}{2})$