Question

PLEASE HELP!!

Answer 1

ΔRST is dilated by a factor of 1/3 with the center of dilation at the origin.The vertices of ΔRST, areR (3, 6)S (-3, 6)T (-6, -6)The vertices of the dilated image ΔR'S'T', areR' (1, 2)S' (-1,2)T' (-2, -2)The transformed image is shown in red color

Answer 2

Answer:

From the given graph:

the coordinates of triangle RST are;

R= (2, 1),

S= (2,-2),

T= (-1,-2)

Given: Scale factor = $\frac{5}{3}$  and center of dilation at (2,2)

The mapping rule for the  dilation applied to the triangle as shown below:    

$(x,y) \rightarrow (\frac{5}{3}(x-2)+2 , \frac{5}{3}(y-2)+2 )$; where k represents the scale factor i.e, $k=\frac{5}{3}$ or we can write it as ;  

For R=(2, 1)      

The image R' = $(\frac{5}{3}(2-2)+2 , \frac{5}{3}(1-2)+2 )$

⇒ R'= $(2, \frac{1}{3})$  

Similarly for S= (2, -2) and T= (-1,-2)

therefore, the image of S'= $(\frac{5}{3}(2-2)+2 , \frac{5}{3}(-2-2)+2 )$

⇒ S'= $(2, \frac{-14}{3})$

The image of T' =$(\frac{5}{3}(-1-2)+2 , \frac{5}{3}(-2-2)+2 )$

⇒T' = $(-3, \frac{-14}{3})$

Now, labelling the image of triangle R'S'T' as shown in the figure given below