Question

Quadrilateral rust has a vertex (2,4). What are the coordinates of r' after a dilation of scale factor 3, centered at the origin, followed by translation (x,y) to (x+4,y)

Answer 1

Answer:

The coordinates of r' are x = 10 and y = 12.

Step-by-step explanation:

The vertex experiments two operations: Dilation and translation, whose definitions are presented herein:

Dilation with respect to origin

$(x',y') = (0,0) + 3\cdot (x,y)$, $\forall \,x,y \in \mathbb{R}$

Translation

$(x',y') =(x+4,y)$, $\forall\,x,y\in \mathbb{R}$

If $x = 2$ and $y = 4$, then:

1) $(2,4)$ Given.

2) $(0,0) + 3\cdot (2,4)$ Dilation with respect to origin.

3) $(6,12)$ Vectorial sum and scalar multiplication.

4) $(6+4,12)$ Translation.

5) $(10,12)$ Vectorial sum. Result.

The coordinates of r' are x = 10 and y = 12.