Question

question
what is the image point of (-5, 3) after the transformation $d_{\frac{1}{3}} \circ t_{-4,3}$?
answer attempt 1 out of 9
(□,□)

Explanation:

Step1: Apply Translation \( T_{-4,3} \)

A translation \( T_{h,k} \) moves a point \( (x,y) \) to \( (x + h, y + k) \). Here, \( h=-4 \), \( k = 3 \), and the original point is \( (-5,3) \). So, \( x=-5+(-4)=-9 \), \( y = 3 + 3=6 \). The point after translation is \( (-9,6) \).

Step2: Apply Dilation \( D_{\frac{1}{3}} \)

A dilation \( D_{s} \) with scale factor \( s \) transforms a point \( (x,y) \) to \( (s\cdot x, s\cdot y) \). Here, \( s=\frac{1}{3} \), and the point from Step 1 is \( (-9,6) \). So, \( x=\frac{1}{3}\times(-9)=-3 \), \( y=\frac{1}{3}\times6 = 2 \).

Answer:

\((-3, 2)\)